Geographic Concentration as a Dynamic Process
Author(s): Guy Dumais, Glenn Ellison and Edward L. Glaeser
Source: The Review of Economics and Statistics, Vol. 84, No. 2 (May, 2002), pp. 193-204
Published by: The MIT Press
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The
Review
of
Economics
and
MAY 2002
VOL. LXXXIV
Statistics
NUMBER2
GEOGRAPHIC CONCENTRATION AS A DYNAMIC PROCESS
Guy Dumais, Glenn Ellison, and Edward L. Glaeser*
Abstract-This paperuses data from the Census Bureau'sLongitudinal
ResearchDatabaseto describethe dynamicsof geographicconcentration
in U.S. manufacturing
industries.Agglomerationresultsfroma combination of the meanreversionandrandomnessin the growthof state-industry
employment.Although industries'agglomerationlevels have declined
only slightly over the last quartercentury,we find a great deal of
movementfor many geographicallyconcentratedindustries.We decompose aggregateconcentrationchanges into portionsattributableto plant
births,expansions,contractions,and closures.We find that the location
choices of new firmsplay a deagglomerating
role, whereasplantclosures
have tendedto reinforceagglomeration.
I.
Introduction
FOR a long time economistshave noted that industries
are often strikingly concentratedin a few states or
metropolitanareas.1There is no shortageof theories explainingwhy this concentrationmay occur(Marshall,1920;
Krugman,1991b), and in recentyears a systematicexamination of the facts has begun (Henderson,1988; Enright,
1990; Krugman, 1991a; Kim, 1995; Ellison & Glaeser,
1997, 1999).
The empirical literatureto date has focused on how
concentratedvariousindustriesare at a point in time, or, in
some cases, such as Fuchs (1962) and Kim (1995), at
multiplepoints in time.2This paperattemptsto add a new
dimensionto the empiricalliterature,moving from a static
descriptionof geographicconcentrationto a dynamicone.
We disaggregatenet changesin concentrationlevels (or the
lack thereof)to examinethe declineof old industrycenters,
the growthof new ones, and industrymobility.Geographic
concentrationis the outcomeof a life cycle processin which
new plants are constantlybeing born, existing plants are
Receivedfor publicationMay 30, 2000. Revisionacceptedfor publication May 10, 2001.
*HarvardUniversity,MassachusettsInstituteof Technologyand National Bureauof Economic Research,and HarvardUniversityand NationalBureauof EconomicResearch,respectively.
Dumaisthanksthe Social SciencesandHumanitiesResearchCouncilof
Canadafor financial support.Ellison and Glaeser thank the National
Science Foundationfor supportthroughgrantsSBR-9818534and SES9601764. They were also supportedby Sloan ResearchFellowships.We
also thankJoyce Cooperof the U.S. Census Bureau'sBoston Research
Data Centerfor a great deal of help, and Aaron Hantmanfor research
assistance.The opinionsandconclusionsexpressedin this paperarethose
of the authorsand do not necessarilyrepresentthose of the U.S. Census
Bureau.
1Some of the classic studies of the phenomenonare Florence(1948),
Hoover(1948), and Fuchs (1962).
2 Beardselland Henderson's1999 study of the computerindustryis a
noteworthyand interestingexceptionto this rule.
expandingand contractingat differentrates,and a substantial number of businesses are failing. We explore these
concentrationover
dynamicfeaturesof U.S. manufacturing
the last 25 yearsusing datafrom the U.S. CensusBureau's
LongitudinalResearchDatabase(LRD).
Analyses of the dynamics of geographicconcentration
may contributeto a numberof often discussedtopics. For
example,Arthur(1986) and Krugman(1991b) emphasize
that,with increasingreturns,industrylocationstodaycould
potentiallybe the resultof historicalaccidentsin the distant
past.3This creates scope for governmentaction and has
implicationsfor understandingsuch questionsas how the
industrialstructureof Europemay changewith integration.
One motivationfor our studyof industrymobilityis thatit
may give a feel for how importanthistoricalaccidentsarein
practice and whether Krugman'scharmingexamples are
representative.A second active discussion concerns the
conditionsthatfavor new businessdevelopment.One view
(associatedwith Marshall,Arrow,and Romer and sometimes referredto as the MAR model) emphasizesthe importanceof increasingreturnsto scale andlearningby doing
and suggeststhatfirmsbenefitfrombeing locatedin industry centers.A second view (associatedwith Jacobs)argues
thatthe most fertileareasfor new plantbirthsareareaswith
a diverse set of relatedindustries.4Variousaspects of our
dynamicdescriptionmay enlightenthis debate.For example, the Jacobsview suggests that industriesmay be fairly
mobile and that startupactivity may be high away from
industrycenters.
Our work is also motivated by the seeming conflict
between the roughlyconstantlevel of geographicconcentrationover the past 130 years (as reportedby Kim (1995))
and the dramaticturnoverof employmentat the plantlevel
documentedby Dunne, Roberts, and Samuelson (1989a,
1989b), Davis and Haltiwanger(1992), and others.5Is this
3 Holmes (1999), in contrast, emphasizes how industriescould be
mobile.
4 See Glaeseret al.
(1992) andHenderson,Kuncoro,andTurner(1995)
for otherempiricalevidenceon the MAR and Jacobsmodels.
5 Thosewho recallFuchs
(1962) mayfindouremphasison stabilitya bit
at odds with his emphasison the decreasein agglomeration.The index
Fuchsuses, however,is problematicin thatone wouldimaginethatit will
tend to decreasewheneverthe plant-levelconcentrationof an industry
decreases.Fuchs, in fact, notes that decreases in agglomerationwere
largestin the fastest-growingindustriesandthatslow-growingandshrinking industrieson averagesaw their agglomerationlevel increase.Kim
(1995) reportsan increasein agglomerationup to 1947 followed by a
The Review of Economics and Statistics, May 2002, 84(2): 193-204
? 2002 by the President and Fellows of HarvardCollege and the MassachusettsInstituteof Technology
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194
THE REVIEWOF ECONOMICS
AND STATISTICS
becausenew plantsjust tendto be foundedacrossthe street
fromold plants,or do thereappearto be forcesthatmaintain
equilibriumlevels of geographicconcentrationdespite relocation?Among our new observationsare that, although
levels of geographicconcentrationare fairlystable,thereis
a clear decline since the early 1980s. Thereare also many
notabledifferencesbetweenindustrygroupsboth in mobility andin the impactof differentlife cycle events.This part
of ouranalysisraisesmorequestionsthanit answers,butwe
hope thatit will motivatefutureresearch.
We begin in section II by presentinga frameworkfor
describingthe dynamicsof geographicconcentration.The
section begins with a review of the static frameworkof
Ellison and Glaeser(1997). We then discuss the measurementof industrymobility.Ourmainobservationhereis that
changes in geographicconcentrationcan be decomposed
into decreases attributableto mean reversion in stateindustryemploymentshares and increases attributableto
randomnessin the process of growth and decline. For
geographicconcentrationto have declined slightly despite
randomnessin the growthprocess,we know thattheremust
be meanreversionin state-industrygrowth.The interesting
unknownsarehow rapidthe declinesof industrycentersare
andhow muchrandomgrowthbolstersconcentration.Subsequently,we discussthe furtherdecompositionof agglomeration changes into componentsthat are attributableto
events at various stages of the plant life cycle: new firm
startups,the opening of new plants by existing firms, the
growth and decline of existing plants, and plant closures.
Whethereach of these stages tend to reinforceor dissipate
concentrationis again an empiricalquestion.
Afterdescribingthe LRD datain sectionIII, we describe
the patternswe find in sections IV and V. Section IV
containsour results on industrymobility.Our most basic
observationis thatindustriesarefairlymobile.By itself this
seems like an importantpiece of evidencein supportof the
idea that observedindustryconcentrationlevels are determinedby equilibriumforces.6The mobilitypatternsdo not
suggest a great role for historicalaccidentsand are more
supportiveof the Jacobs view than they are of the MAR
view. Richerpatternsappearin examiningdifferentsubsets
of industries.The textile industries,for example, are a
noteworthyexceptionto the generalpatternandexhibitlittle
mobility.
Section V containsour resultson geographicconcentration and the plant life cycle. One of the more striking
findingsof this sectionis that,althoughnew plantbirthsare
higher in areas where an industry is concentrated,the
increaseis substantiallyless thanone for one. In fact, new
plantbirthsaresufficientlydispersedso as to act on average
decreasefrom 1947to 1987,withthe largestpartof the decreaseoccurring
between 1947 and 1967.
6 Otherkey pieces of evidence supportingthis view are Kim's 1995
findingthat 1860 and 1987 agglomerationlevels arehighlycorrelatedand
Maurel and Sedillot's 1999 finding of correlationbetween levels of
agglomerationin the UnitedStatesand in France.
to reduce geographicconcentration.Althoughthe lack of
concentrationof new plantbirthsin old industrycentersis
somewhatsupportiveof the Jacobsview, the deagglomeratingrole thatbirthsplay does not supporta modelin which
concentrationis maintainedby clustersof new firmbirths.
The expansionandcontractionof existingplantsalso on net
acts to reduceagglomeration.The one life cycle stage that
acts to maintainagglomerationis the plantclosureprocess:
plantsin industrycentersare less likely to close. Existing
theoriesagain do not seem to capturethis well. We again
look in detail at various industrygroups and at different
time periods.
II.
A Framework for the Dynamics
Geographic Concentration
In this section, we brieflydiscuss Ellison and Glaeser's
(1997) index of geographicconcentrationand then introduce two decompositionsof concentrationchanges. The
first of these focuses on industrymobility,and the second
focuses on events at variousstages of the plantlife cycle.
A. Background:The EG ConcentrationIndex and Some
Facts
The Ellison and Glaeser (hereafter,EG) index of the
degreeto whichindustryi is geographicallyconcentratedat
time t is given by
Git,/(1
-
s2t)- Hit
ee
iht
sist is the share of industry i's time t employment located
in state s,
Git
I s (Sist - sst)2 is a sum of squared deviations of
the industry's state employment shares Sist from a
measure,st, of the states'sharesof employmentin the
averageindustry,and
measureof the plant-levelconHit is a Herfindahl-style
centrationof employmentin an industry:Hit,
k
eikt)2 where eikt is the level of employmentin
e2t/l(k
the kth plantin industryi at time t.7
The motivationfor the EG index is that it is an unbiased
estimateof a sum of two parametersthatreflectthe strength
of spilloversand unmeasuredcomparativeadvantagein a
benchmarkmodel. Underparticularassumptions,the index
is independentof the number and size of plants in the
7 In a slightdeparturefromEllison andGlaeser(1997), the measuresst
we use here is the unweightedarithmeticmean of the sist across the
industriesin our sample;that is, sst = (1//) Ei sist whereI is the total
numberof industries.The use of the unweightedmean facilitatesthe
developmentof an unweighteddecomposition,which we feel providesa
moreinformativereflectionof the dynamicsof concentrationin a typical
industry.
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CONCENTRATION
AS A DYNAMICPROCESS
GEOGRAPHIC
industryand of the geographicdivisions used to form the
measure.
In practice,changes in the value of the EG index over
time are well approximatedby changes in the difference
betweenGit andHit. Ellison andGlaeser(1997) referto Git
as the raw geographicconcentrationof employmentin an
industry.The subtractionof Hi, is a correctionthataccounts
for the fact that the Git measurewould be expected to be
larger in industries consisting of fewer larger plants if
locationswere chosencompletelyat random.Becauseplant
size distributionstendto changefairlyslowly,the correction
is less importantin cross-timecomparisonswithin a short
time periodthanin cross-industrycomparisons.
Beforeproceedingwith the developmentof ourmeasurement framework,it will be useful to have seen a few facts.
The first row of table 1 reports the mean across U.S.
three-digitmanufacturingindustriesof the EG index (as
computedfromdataon employmentat the statelevel.) The
overall patternis that concentrationof the mean industry
remainedfairly constantbetween 1972 and 1982, and then
fell by approximately10%in the following decade.
The second and thirdrows of table 1 give the means of
GitandHit from 1972 to 1992. These show thatthe decline
in the EG index is associatedmainlywith a decreasein raw
geographicconcentration.Althoughthereis no clear trend,
the averageplant-levelHerfindahlis slightlyhigherin 1997
thanin 1972. Hence,the decline in the EG index is slightly
largerthanthe decline in raw concentration.Table2 illustrates a second importantfact: the substantialdifferences
that exist in concentrationacross industrieschange little
over time. The correlationof EG indices measuredfive
years apartis approximately0.97, and the correlationbetween the 1972 and 1992 values is 0.92. Thus,the ongoing
dynamicprocess somehowmanagesto maintainfairly stable levels of agglomeration.This stability is even more
strikingin Kim's 1995 calculationof Hoover's coefficient
of regionallocalizationfor two-digitindustries.The correlationbetweenthe 1860 and 1987 values of the localization
coefficientshe reportsis 0.64.
B. Geographic Concentrationand IndustryMobility
195
TABLE2.-CORRELATIONOF ELLISON-GLAESER
INDEXOVERTIME
(1972-1992)
1977
1982
1987
1992
1972
1977
1982
1987
0.973
0.967
0.918
0.917
0.973
0.924
0.925
0.969
0.962
0.975
The table gives the correlationbetween the values of the EG index when computed using data from
different years.
old plants at the same location, so state-industryemployments do not change;or, alternatively,some equilibrating
forcesmaykeep agglomerationroughlyconstanteven while
the industries'locations are changing greatly. Here, we
develop a simple framework for thinking about how
changesin agglomerationwill resultfroma combinationof
the systematicgrowthand contractionof old industrycenters and randomnessin growthrates.
Considerthe following simple regressionin which we
treat the change in state-industryemploymentshares (for
example, the share of industryi's employmentlocated in
state s) as a functionof the growthof the state's average
employmentshare(thatis, the averageacrossindustriesof
the share of employmentin state s) and the difference
between initial state-industryshareand the state's average
employmentshare:
Sist+1 -
Sist
= di +
{(sist-
s,)
+ y(Sst+1 - Ss,) + Eist,
(1)
where
Sistis the shareof industryi's employmentin states as of
time t,
sst is the average of this variable for state s across
industries,
&, p, and ^ are estimatedcoefficients,and
Eist is an estimatederrortermwhich is, by construction,
orthogonalto each of the regressors.
The combinationof turnoverat the plant level and stability in agglomerationlevels is compatiblewith a wide Note that this regressionis specified so that each of the
rangeof mobilitypatternsbetweentwo extremes:agglom- variableshave meanzero and so thatthe two regressorsare
erationcould be constantbecause new plantsjust replace
orthogonal.As a result, the OLS estimateswill always be
that a = 0 and ' = 1.
TABLE1.-MEAN LEVELS
OFGEOGRAPHIC
CONCENTRATION
1972-1992
Ellison-Glaeserindex (y)
Raw concentration(G)
Plant Herfindahl(H)
Employmentweighted mean y
1972
1977
1982
1987
1992
0.039
0.049
0.013
0.038
0.039
0.049
0.012
0.038
0.038
0.049
0.012
0.037
0.036
0.046
0.012
0.035
0.034
0.045
0.013
0.034
The table reportsmeans (across 134 U.S. three-digitmanufacturingindustries)of the Ellison-Glaeser
index of geographic concentration and two components: the simpler raw geographic concentration
measure and a Herfindahlmeasure of plant-level concentration.
In this section,we will analyzechangesin agglomeration
levels using the raw concentrationcomponent,Gi, of the
EG index of concentration.8
WriteGt (1/I) Xi Gi, for the
8 As we noted
previously, the trends in raw concentration and in the EG
index are fairly similar. Focusing on raw concentration rather than on the
EG index allows us to bring out the main observations of this section more
simply. We will discuss a more complex decomposition that also accounts
for changes in plant-level concentration in the next subsection.
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AND STATISTICS
THE REVIEWOF ECONOMICS
196
mean of this variable across industries.Simple algebra people's heights to remainroughlythe same over time, it
revealsthat
mustbe the case thatchildrenof tall parentsare on average
shorterthantheirparentsand childrenof shortparentsare
1
on
averagetallerthantheirparents.
- G =
Gt+i
I
is
(Sist+l
Eis (Sist
st+l)-
s
C. Geographic Concentrationand the Plant Life Cycle
1 Eis ((1 +
=
P)Sis,
I
+ Eist-
st+1)2
(2p
+ p2)
"=
=(21+
2
-
2)Gt+
- PSs + 9(sst+l- st)
is
is
(Sist - St)2
(Sist
-
Sst)2+
is
f22st
Ii,st.
I is
This equationdecomposeschangesin concentrationinto
the sum of two terms,which we will describeas the effects
of mean reversion and of randomness (or dispersion) in the
local employmentprocess.The first term in the decomposition, (2P + [32)Gt, dependson the extent to which net
change in employmentis correlatedwith the initial gap
betweenthe state-industry
employmentshareandthe state's
share of employmentin the averageindustry.When 3 is
negative, currentcenters of the industryare declining in
importanceand/or employmentis tending to increase in
areasthat initiallyhave a below-averageshareof employment in the industry.In this case, we will describe the
state-industry
employmentlevels as displayingmeanreversion, andthe firsttermin the decompositionis the decrease
in agglomerationthatis attributableto this tendency.Conversely,when p is positive and industrycentersare growing, the firsttermreflectsa consequentincreasein agglomeration.
The second term in the decomposition, 2is
E2t,
captures
the effect of randomnessin the growth (and decline) in
state-industryemployments.The magnitudeof this componentreflectsthe degreeof heterogeneityin the experienceof
states that initiallyhave similarconcentrationsof employment in a given industry.For example,it will be largerif
some industrycenterstakeoff while othersfail, andif some
areaswherethe industryis not presentarevery successfulin
attractingnew plants while others are not. This term is
always positive: randomnessof the growth process can
always be thoughtof as increasingagglomerationlevels.
For the overalllevel of agglomerationin U.S. manufacturing to have declinedslightly over the last twenty years, it
must be that p is negativeso thatthe agglomeratingeffect
of randomshocks has been counterbalanced
by systematic
meanreversion.
The role of meanreversionof state-industry
employment
and randomshocks in maintaininga steady level of concentrationovertime is analogousto the classic discussionin
statistics courses of the fact that, for the distributionof
A new geographiccenter of activity in an industrycan
develop in a numberof differentways: the area can be a
hotbedfor startupfirms,it may succeedin attractingthe new
plantinvestmentsof existingfirms,or a core of preexisting
firms may grow into a position of prominence.In this
subsection, we describe a decompositionof changes in
agglomerationinto portionsdue to variouslife cycle events.
Supposethatthe dataallow the employmentchangein a
state-industryto be partitionedinto portionsattributableto
one of J categoriesof events (such as to new plantbirths,
plantclosures,and so on):
Eist+l - Eist =
J
AEJs
whereEist is the employmentlevel of industryi in states at
time t, andAEj,tis the changein employmentdue to events
of typej. Denoteby AE!t the aggregateamountof employment changedue to thejth growthprocess.
In the previoussubsection,we focused on a simple raw
concentrationmeasure of geographic concentration.We
justifiedthis by noting that it is an empiricalfact that the
overalldistributionof plantsizes has not changedas much
over the last twenty years. Such an argument,however,
cannotjustify ignoringchangesin plant Herfindahlswhen
decomposingconcentrationchanges into portionsattributable to various life cycle stages. Although the overall
plant-levelconcentrationof industrieshas remainedroughly
constant (using the plant Herfindahlmeasure),new firm
births clearly tend to reduce this concentrationand plant
closures tend to increaseit. Hence, the effect of birthsor
closureson raw concentrationand on the EG index may be
quite different.
To obtain a tractabledecomposition,we focus on a
measureof agglomeration,y, which closely approximates
the EG index:
- it
1-1 -
i
2
-
s s Ht
Hit.
(The approximationinvolves ignoringthe 1 - Hit denominator of the EG index.9) Writing Gt =
it
Git for the
averageraw concentrationacrossindustries,we firstdefine
in equation(3) a decompositionof the aggregatechangein
9 Ignoring changes in the denominator makes decomposing concentration changes straightforward.The changes in H attributableto the various
stages of the life cycle typically have a magnitude of approximately 0.001.
Hence, ignoring the denominator will not change in a meaningful way our
description of the effects of the various life cycle changes.
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J
GEOGRAPHICCONCENTRATIONAS A DYNAMIC PROCESS
raw concentration into portions attributable to events in
each of the J categories; that is, we define measures AG,
such that Gt+i - Gt = 2J= AG'. Next, in equation (4), we
define a similar decomposition of changes in the average
plant Herfindahl: Ht+1 - H, = EJ=L AH. Our final
measure of the portion of the change in the index
i 'Yit attributableto
t'Y=
197
previous section. The aggregate change in raw concentration is related to the parameters of these regressions by
G, = (2 + P)1Gt +
G+l-
I
A
the jth stage of the life cycle is
j (2
st
E
is
I
E
ist
)Gt
Eist
then just
= E AG7,
J
AGJ
- AHt.10
Ail-
where the change in raw concentration due to events in the
To decompose raw concentration changes, we first define jth category is defined by
a measure, Asist, of the portion of the change in state s's
share of employment in industry i that is due to the jth
AG] ( j(2 + )Gt +I Es Eistst
(3)
growth process by
A
A-1"
I^
st
AEis - sistAEit
i
As motivation for this definition, note that AG, is a sum
of four terms:
~~17
1
The numerator of the right-hand-side contains a difference
of two terms: the actual employment change due to the
events of the jth type and the employment change that
would have resulted if events of the jth type had occurred in
proportion to initial state-industryemployment. The denominator is end-of-period industry employment. If, for example, new firm births in an industry occurred proportionally
to the initial state-industry employments (and there were no
differences in the size of new firms across states), then there
would be no changes in state-industry employment shares
caused by new firm births, and Asnbith would be zero for
each state. Because state-industry shares change nonlinearly
with changes in each plant's employment, our partition of
share changes into portions attributable to each of several
factors is by necessity arbitrary.We believe, however, that
this definition seems natural, and it satisfies the crucial
adding-up constraint: Sist+ - Sist = 2j Asist.
We then estimate for each of the J categories of employment changes a growth regression of the form
ASst
=
j
+
-
3j(Sit
Sst) +
(Sst+l -
Sst) +
st
(2)
The estimates from these regressions will satisfy Ej 3j = B,
' and ist =
Ej /j =
-j eJst where p, ', and eist are the
estimates from the employment change regression (1) of the
AGi = (2,j + P2)Gt,+
+
I
I
eit +
ip
2 PkGt
k-j
E st
E
is
is
k-j
The first two terms reflect the change in concentration due
to the mean reversion and randomness in employment
changes of type j. The third and fourth terms are what we
thought was a natural allocation of the additional agglomeration changes that result from correlations between employment changes due to events of type j and due to events
of other types.
The decomposition of changes in the plant Herfindahl
index into portions due to events at each stage of the life
cycle is analogous with plant-industry employments taking
the role of state-industry employments. Let eikt be the
employment level in the kth plant in industry i at time t. We
write Zikt
-
eiktl/k eikt
for plant k's employmentshare
within its industry. Our plant Herfindahl measure for industry i can be written as Hit = Ek Z2t. We write
Ht =
, , Hi for the average of this measure across
industries.We write Aikt
Zikt+ 1 -
Zikt for the changein
10Note that our definition of A/j ignores the effect on measured plant k's employment share, with the convention that Ziktis
concentrationof changesin the denominator1 - s s2. For this reason, set to zero if plant k is not in industry i at time t. (For
although our decompositions satisfy Gt+l - G, = AJ=1aG and Ht+1 example, AZikt = -Zikt if the kth plant in industryi has
Ht = ZJ=I AH', the sum of the A-i will not be exactly equal to /t+l switched to another industry at time t + 1.)
yt. The differencewill be smallif changesin Es s,t aresmall,thatis, if the
Assume again that we have a partition of employment
distributionof state sizes does not change much over each five-year
period.It wouldbe tedious,but not difficult,to derivea decompositionof changes in each plant-industry into portions attributableto
A-I thatdoes add up exactly.The differencebetweenA,t and E, At as events in each of J
categories:
we've definedit is equal to Gt+1 (Es s,+ Zs
s,)/((1 -Es s,2)(1 Es s,,+i)). This term could be decomposedinto portionsattributableto
eachof theJ life cycle stagesin a manneranalogousto ourdecomposition
of changesin the plantHerfindahl.
Aeik
=
EAejik
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198
THE REVIEW OF ECONOMICS AND STATISTICS
census or does so with zero reported employment. We
obtain our first two categories of employment change by
classifying the birth of an establishment that is not part of a
firm
Aekt - ZiktAEjt
owning other establishments covered by the Census of
AZ kktManufactures as a "new firm birth," and the birth of an
Eit+ 1
establishment that is owned by a firm that had establishThis definition again yields an allocation of share changes ments in previous censuses as an "old firm birth."1'Using
across the categories; that is, Zikt+ - Zikt = >j iAZktrWe this distinction, an average of 87% of all newly created
then estimate separate employment change regressions for plants in our four five-year intervals can be classified as new
each of the J components of changes in the plant-industry firm births. These plants are smaller on average than the
employment shares,
plants opened by existing firms and account for approximately 50% of employment growth due to plant births. Our
= ' + IjZikt+
kAZtk
third category of employment change is the net expansion
E^kt,
and contraction of plants that had positive employment in
- N for Ni, the number of plants that the industry at time t and that are still in operation with
where Z,kt Zi,
strictly positive employment at time t + 1. Our fourth
operate in the industry either in period t or in period t + 1. category, plant closures, consists of all changes attributable
We show in the appendix that the definition analogous to to
plants that had positive employment in the industry at
our definition of AGt,
time t and have zero employment or do not appear in the
time t + 1 census. Finally, to make the employment
- I- 2 N
add up to the total employment change, we need a
AHi t(2pj + jp)(H
I
changes
)
fifth category: switches. This category includes all employment losses or gains in an industry that are attributableto
(4)
E i?+
E
E 6 ikt ( E
ik
plants that were classified as belonging to the industry at
lk
I ik
j
time t being classified as belonging to another industry at
t + 1 and vice versa.12Although some of these switches
again provides a decomposition that satisfies
undoubtedly reflect real changes in the activity of plants,
- H = E AHj.
others are likely just reclassifications, thus, we will only
Ht+
briefly discuss results on switches.13
We measure the level of economic activity in an industry
m. Data
in a given area by total employment in all manufacturing
establishments excluding auxiliary units. We use the fifty
The main data used in this paper come from the U.S.
U.S. states plus the District of Columbia as our geographic
Census Bureau's Longitudinal Research Database. The
units. At the industry level, we examine 134 manufacturing
LRD is a longitudinal microdata file that links the informaindustries corresponding to three-digit industries in the 1987
tion obtained from the manufacturing establishments inIndustrial Classification (SIC).14
cluded in the quinquennial Census of Manufacturers(since Standard
1963) and the Annual Survey of Manufactures (since 1972).
1 These new firmbirthscould be connectedto firmsthatexisted in the
McGuckin and Pascoe (1988) and Davis, Haltiwanger, and
We
previouscensus year but did not have a presencein manufacturing.
Schuh (1996) provide a detailed account of the information believe, however, that a large majorityof these plants representtrue
and the formationof a new firm,not just a new plant.
found in this data set. In this study, we focus the analysis on entrepreneurship
12
in how one allocatesthe growthof plants
is some arbitrariness
the five census years since 1972 (1972, 1977, 1982, 1987, thatThere
both changeemploymentand switch industries.The conventionwe
and 1992), using 1972 as a base year. This provides between have adoptedis to assignthe full net expansionto the initialindustry.For
312,000 and 370,000 observations in every census year, example,if a plantis listed as havingone hundredemployeesin industry
A at time t and eightyemployeesin industryB at time t + 1, we regard
covering every manufacturing establishment in the United industryA as havinglost twentyemployeesin a contractionandeightyin
States. We will briefly address some of the major features of a switch and industryB as havinggainedeighty employeesin a switch.
13 See McGuckinand Peck (1992).
this data set here.
14The
industriesexcept SICs 211,
sampleconsistsof all manufacturing
One of the advantages of the LRD is that it makes it
212, 213, 214, 237, and 381. The firstfive of these were omittedbecause
to plantsbeingreported
possible to follow a plant through the stages of its life cycle. therewerelargeemploymentchangesattributable
Our analysis will focus on a breakdown of employment as having shiftedbetweenthe industryin questionand a closely related
industry,for example,betweenthe fur industryand the women's outerchanges into five categories: births of new firms, the open- wear industry.We felt thatthese switchesmay well have been reclassifiing of new plants by existing firms, the expansion or cationsratherthanreal changes,and, becausethe industriesin question
contraction of existing plants, plant closures, and switches were also fairly agglomerated,we worriedthat they could have a large
on ourresults.The searchandnavigationequipmentindustry(381)
of plants between industries. We define a plant birth be- effect
was excludedbecauseof a majordiscontinuityin employmentsover time,
tween time t and time t + 1 as a plant that appears in the which mightbe due to recodingin the yearspriorto 1987 to makethem
time t + 1 census and either does not appear in the time t consistentwith the 1987 SIC.
As before, we define the portion of the change in each
plant's share of employment to events in each category by
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GEOGRAPHICCONCENTRATIONAS A DYNAMIC PROCESS
199
TABLE3.-PATTERN OF RAW CONCENTRATION
CHANGESACROSSINDUSTRIES
Set of Industries
[Numberof Industriesin Brackets]
Mean y
(1972)
AveraTgeCorrelatlon
between 1972 and 1992
State Shares
Full sample [134]
Geographicallyconcentrated[45]
Geographicallyunconcentrated[45]
Concentratedhigh technology [6]
Concentratednaturalresource [11]
Concentratedtextile & apparel [14]
Concentratedcrafts [6]
0.039
0.088
0.006
0.103
0.052
0.111
0.048
0.86
0.88
0.86
0.82
0.90
0.88
0.79
Average Five-year Percentage
Change in Raw Concentration
Estimates
13
-0.062
-0.043
-0.116
-0.065
-0.059
-0.015
-0.064
a
Total
Mean Reversion
Dispersion
0.010
0.010
0.008
0.013
0.007
0.010
0.011
-2.4
-2.5
-0.1
-4.8
-5.7
2.1
-1.6
-12.0
-8.4
-21.7
-11.9
-11.1
-2.8
-12.2
9.6
5.9
21.5
7.0
5.4
4.8
10.7
The table reportsa numberof statistics relatingto industrymobility.The first column gives mean EG index for the set of industriesin 1972. The second reportsthe average correlationbetween each state's share
of the industry'semploymentin 1972 and 1992. The thirdand fourthcolumns presenta coefficient estimateand the estimatedresidualstandarddeviationfrom regression(1). The final threecolumns reportthe average
percentagechange in raw geographic concentrationattributedto mean reversion and dispersion as described in subsection UB.
Obviously, many other choices were possible. In industrial organization, a three-digit industry definition is
usually regarded as too broad. We agree wholeheartedly
in the context of defining industries to study product
marketcompetition. For example, the four-digit classification divides the three-digit men's clothing industry
(SIC 323) into subcategoriessuch as men's shirts, underwear, neckties, trousers, and work clothes. A consumer
who wants a shirt is clearly unlikely to buy a pair of
underwearinstead. The four-digit industriesare less distinct, however, on the production technology side. The
same plant may produce products in several four-digit
industries,and it is not uncommonto see plants coded as
belonging to different industries in different censuses.
Changes due to plants switching industries are very large
in a decomposition of changes in the concentration of
four-digit industries. It is less common to see plants
codes as switching between three-digit industries, and we
felt that decompositions based on the three-digit definition provided a clearer picture. Ellison and Glaeser
(1997) note that in 1987 the mean EG index is similar
when measured using three- or four-digit industries (the
means are 0.045 and 0.051, respectively) and discuss the
extent to which the four-digit subindustries of three-digit
industries are coagglomerated.
The choice of the geographic unit is more arbitrary.
Some agglomerations are very tight and some involve
plants spread over a large area. A state-based measure
would have failed to identify, for example, the classic
agglomeration of glove-making firms around Gloversville, New York, in the late nineteenth and early twentieth
century. A county- or MSA-based measure would not
reveal the full extent of the agglomeration of pharmaceutical firms in New Jersey or of automobile manufacturers
in Michigan. Ellison and Glaeser (1997) describe the
frequency with which agglomerations seem to be a
county, state, and regional phenomenon. Our focus on
state-level agglomeration makes our results comparable
to the largest part of the evidence in Ellison and Glaeser
(1997).
IV.
Geographic Concentration and the Movement of
U.S. Manufacturing Industries: 1972-1992
As we noted earlier, the stability of geographic concentration is consistent with two very different mobility patterns: agglomeration could be constant because new plants
just replace old plants at the same location, or, alternatively,
some equilibrating forces may keep agglomeration roughly
constant even while the industry's locations are changing
greatly. Arthur (1986) and Krugman (1991b) emphasize the
potential for locations to be locked in by historical accidents
with all the accompanying possibilities for inefficiency.
Holmes (1999) notes that MAR externalities can also be
compatible with industry mobility.
Table 3 contains parameter estimates for the stateindustry employment change regression (1) for different
subsamples of industries. Observations from all four periods
have been pooled in each subsample. The first column gives
the average EG index of each subgroup. The second gives
the correlation between each state's shares of each industry's employment in 1972 and 1992. Note that these are
quite high, although not as high as the 0.92 correlation
between 1972 and 1992 values of the EG index. For the
entire sample, the estimated coefficient (3 on the departure
of the state-industry employment share from the average
employment share is -0.063. Hence, over the twenty-year
period, states in which an industry is initially overrepresented in an area would be expected to experience a decline
in its excess employment of nearly one-fourth.
The sixth and seventh columns of the table present our
decomposition of how much of the change in concentration
is attributable to mean reversion and to dispersion in the
employment change process. In the full sample, the mean
reversion effect is sufficiently strong so as to produce a 12%
decrease in agglomeration every five years, while the dispersion effect by itself would lead to a 9.6% increase. The
effects almost balance each other and result in the net
negative of -2.4%. The magnitudes of the two separate
effects indicate that there is a substantial degree of industry
mobility relative to the degree to which concentration levels
have changed. This view contrasts with the emphasis of
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200
AND STATISTICS
THE REVIEWOF ECONOMICS
CHANGESAND INDUSTRY
TABLE4.-RAW CONCENTRATION
some previousauthors(Krugman,1991a) on historicalacMOVEMENT OVER TIME
cident.
PercentageChange in Raw Concentration
There are clear differencesin the employmentchange
Total
Mean Reversion
Time Period
Dispersion
patterns in different groups of industries. In the highconcentrationsubsample(whichcontainsthe most-agglom8.3
-1.3
-9.6
1972-1977
8.9
-1.4
-10.3
1977-1982
eratedthirdof industriesaccordingto the 1972 EG index),
12.3
-4.3
-16.6
1982-1987
overall
that
of
the
than
is
smaller
that
we estimate a p
9.0
-11.7
-2.7
1987-1992
sample.Perhapssurprisingly,thereseems to be no moreor The table presentsthe decompositionof changes in raw concentrationdescribedin subsectionIIB for
less randomnessin the growthprocessof this subsample(as four separateperiods.
measured by &) than in the full sample. The lowconcentrationsubsample(which containsthe least-concentratedthirdof the industriesin the sample)is distinguished
half of the periodthanit was in the first,andthus the more
by havingmuchstrongermeanreversion;the estimated, of
-0.116 indicatesthat,on average,areasin which an indus- rapiddecline in agglomerationthat has takenplace in the
last half of the periodcan be more thancompletelyattribtry was overrepresentedsaw their excess employmentre- uted to an increase
in the rateat which old industrycenters
ducedby approximately40% over the twenty-yearperiod.
to
decline.
have
tended
The final four lines of the table are concernedwith the
Overall, the most importantlesson is that (outside of
behaviorof four sets of industrieswith moderateto high
textiles)
manyconcentratedindustriesarequitemobile.The
concentration.Three of the four groups display about as
that
concentrationdoes not simply take the form of
fact
much mean reversionas the averageindustry(geographinever moving is strong evidence that levels of
industries
cally concentratedor not). We constructedthese samples
concentrationare an equilibriumphenomenon
geographic
manuallyin an attemptto categorize the industriesthat whetherdue to
increasingreturnsor cost differences.Moappearedat the top of our concentrationlist. The four
with Jacobsor MAR externalities
is
not
incompatible
bility
samplesincludethe majorityof the industriesin our "geo- but would lead us to
the importanceof distant
downplay
graphicallyconcentrated"sample (as well as some others historicalaccidentsfor
industries.
concentrated
many
thatareonly slightlyless concentrated).The one subsample
which is very differentis the set of textile industries(conV. Agglomeration and the Plant Life Cycle
sistingof industrieswithinSIC groups22 and23 for which
the 1972 EG index was in the top sixty). In these industries,
In this section,we discusshow eventsat variousstagesof
thereis muchless meanreversionthanin the otherconcen- the plant life cycle have contributedto the geographic
tratedindustries,and the degree of concentrationhas risen concentrationof U.S. manufacturingindustries.One motiover time. In each of the othersubsamples,raw concentra- vation for this exercise is the basic desire to understand
tion levels have declined. The behavior of the high- wherein the life cycle concentrationarises,how the dynamindustriesdiffer,and
technology subsampleis fairly similar to the full sample ics of concentratedandunconcentrated
with the one noteworthyfeaturebeing thatthereis a larger why geographicconcentrationhas begun to decline in the
random componentin the employmentchanges.15(This last decade. Anotheris the desire to explore the contrast
randomness,however, is not sufficiently large so as to between the MAR emphasison within-industryspillovers
sustainthe high initial level of agglomeration.)The set of and the Jacobsemphasison diverseenvironmentscreating
industriesfor which we imaginednaturalresourcesmay be hotbedsfor startupactivity.
relevantto agglomeration(includingseveralfood, lumber,
Ouranalysisof datafromthe LRD focuses on a descrippaper,petroleumand primarymetalsindustries)appearsto tion of employmentchangesas resultingfrom five categohave substantiallyless randomnessin the growth and de- ries of events:birthsof new firms,openingsof new plants
The patternin the craftindustries by existing firms,the growthor decline in employmentat
cline of state-industries.16
is quite similarto the patternin the full sample.17
existingplantsthatcontinueto operatein the industry,plant
Table4 reportsseparatedecompositionsof the declinein closures, and switches of plants from one industryto anraw concentrationinto componentsstemmingfrom mean other. Somewhatsurprisingly,we will see that new firm
reversionandfromdispersionfor each of the fourfive-year birthsand expansionsof existing plantshave a deagglomintervalsin our sample. In all four periods,concentration erating effect whereas the plant closure process tends to
declines, but the change has been most pronouncedsince reinforceconcentrationlevels.
1982. The dispersioneffect has been largerin the second
A. Overall Patterns
15 The
concentrated high-technology sample consists of SICs 357, 365,
372, 376, 385, and 386.
16 The concentrated natural resource
sample consists of SICs 203, 207,
241, 242, 243, 261, 262, 291, 331, and 332.
17 The concentrated crafts
sample consists of industries 326, 328, 387,
391, 393, and 396.
Table 5 lists the coefficient estimates from regressing
each component of employment change, Asp,, on the initial
excess concentration of the industry in the state, Sist - st,
and on the overall growth of the state, Sst+l - Sst as in
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GEOGRAPHICCONCENTRATIONAS A DYNAMIC PROCESS
201
ATVARIOUS
TABLE
5.-EMPLOYMENT
CHANGES
LIFECYCLE
STAGES
Independent
Variable
Sist -
Sst
Sst+l - SSt
R2
U(X 100)
Dependent Variables:Componentsof Employment Share Changes, Asi,,
Total Change
New Firm Births
Old Firm Births
Closures
Expansions/Contractions
Switches
-0.062
(0.002)
1.000
(0.023)
0.05
0.95
-0.023
(0.0004)
0.174
(0.005)
0.11
0.22
-0.018
(0.0006)
0.198
(0.007)
0.05
0.31
0.024
(0.001)
0.138
(0.012)
0.02
0.51
-0.031
(0.001)
0.488
(0.014)
0.07
0.56
-0.014
(0.001)
0.002
(0.016)
0.00
0.65
The table presents estimates from six regressions each having the form described in equation (2). In the first column, five-year changes in a state's share of industryemployment are regressed on the "excess"
share of employment in that industryin the state in the initial year and a measureof state growth. The next five columns reportsimilar regressionsfor dependentvariablesthat are the portion of the total five-year
change attributedto events at each of five stages of the plant life cycle. Standarderrorsare in parentheses.
equation (2). For the new firm birth and old firm birth theoretical literatureon geographic concentration, this result
regressions, the coefficient on Sist - Sst is negative, particularly merits attention.18
indicating that there is mean reversion in employment
shares: employment in new plants (especially those be- B. Changing Patterns over Time
longing to new firms) increases less than one-for-one
One of our initial observation from table 1 was that the
with state-industry employment. The coefficient on initial
trend
toward industries being less geographically concenexcess employment is positive in the plant closure retrated
has been more pronounced in the second half of our
gression, indicating that plants are less likely to close in
in
states that have a higher than expected share of the sample than the first. The average across industries of the
value of the EG index was 0.039 in 1972, 0.038 in 1982, and
industry's employment. (The dependent variable is neg- 0.034 in 1992. From table
6, we see that this change is
ative in this regression.) For expansions and contractions,
attributable
to
the
fact
that differing plant closure
the X coefficient is also negative, implying that growth largely
rates ceased to reinforce initial concentrations and to an
rates are lower in states with a high initial concentration
increased tendency for plant expansions to occur away from
in the industry. New firms are more likely to start away
centers. The effect of new plant births has been
from current geographic centers of the industry, and industry
constant
fairly
throughout the period we study.
growth is faster away from those centers, but the risks
appear to be higher in the periphery and closures are also C.
Differences across Industries
higher there.
Table 6 reports the portions of the change in the approxTable 7 reports the results of performing the same life
imate EG index, It, which we attribute to each of the life cycle decomposition calculation for various subsets of incycle stages. These changes are listed as a percentage of dustries. In this calculation, we have chosen to measure
initial concentration in the set of industries; that is, the table agglomeration in these industries relative to the same basereports values of 100A,/yt. Again, new firm births con- line state shares s,, as we used in the full sample.19In each
sistently have the effect of reducing the degree to which
18In preliminarywork we obtained similar results when
industries are geographically concentrated. On its own, the
examining
threefour-digitindustries.All stages otherthanplantclosureswere
deagglomerating effect of new firm births can account for foundand
to reduce agglomeration,and new firm births had the largest
approximately three-fourths of the observed decline in geo- deagglomeratingimpact.The regressionon which our decompositionis
graphic concentration over the last twenty years. Although baseddoes not have controlsfor differencesin the age andsize of plants.
Plantsin
centerstendto be olderandlargerthanthe averageplant
plants opened by preexisting firms are comparable to new in an industry
andhenceone mightexpectthembothto growmoreslowly
industry,
firm births in their total employment, they have less of a and to be less likely to close. Table 8 of Dumais,Ellison, and Glaeser
deagglomerating effect: they reduce geographic concentra- (1997) presentsregressions(usingMSA-leveldata)thatindicatethatthe
tion in only three of the four five-year periods. On average, findingthatplantsin industrycentersare less likely to close is robustto
the inclusionof controlsfor a plant'sage andsize, but thatthese controls
their effect is only a little more than one-third as large as the may accountfor the slowergrowth
of existingplantsin industrycenters.
Our finding that new and old firm births increase substantiallyless
effect of new firm births.
with initial employmentalso comes throughclearly in the
Consistent with our previous finding that net expansions one-for-one
MSA-level regressions.
are lower in areas with an excess concentration of employ19Because sst is not the average of the state-industry shares across the
ment in an industry, we find that net expansions also tend to industries in the subsample, the portions of the total change attributed to
each of the life cycle stages will not add up, even in an approximate sense.
reduce geographic concentration. The magnitude of this We
felt, however, that this was preferable to setting the ss, equal to the
effect is roughly comparable to that of new firm births. The mean shares within the subsample, as this would implicitly be defining,
one growth process that appears to reinforce geographic agglomerated to mean that a textile industry's employment distribution
differed from that of the typical agglomerated textile industry. This would
concentration is the closure process. Given that plant clo- make us
regard a textile industry that was evenly spread throughout the
sures have not been explicitly discussed in the existing United States as agglomerated, for example.
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202
THE REVIEW OF ECONOMICSAND STATISTICS
TABLE
6.-LIFE CYCLE
DECOMPOSITION
OFCHANGES
INGEOGRAPHIC
CONCENTRATION
Time Period
Change in y, Attributedto:
~Percentage
~~~Percentage
Percentage _~~
New Firm Births
Old Firm Births
Closures
Change in IYt
Expansions/Contractions
1972-1977
1977-1982
1982-1987
1987-1992
Average of estimates
-2.1
-2.8
-2.3
-2.7
-2.5
0.4
-2.7
-5.9
-4.7
-3.2
-1.8
-0.8
-1.2
0.2
-0.9
2.9
2.6
-0.1
0.6
1.5
-0.7
-2.8
-2.4
-2.9
-2.2
Switches
2.2
1.2
0.2
0.4
1.0
The first column of the table gives the percentagechange over each five-year period of the average (across 134 three-digitmanufacturingindustries)of the g measureof geographicconcentration.The final five
columns decompose these changes into portions attributableto events at various stages of the plant life cycle. The decomposition is described in subsection UC.
VI. Conclusion
case, we reportthe averageof the effect in each of the four
five-yearperiods.
The geographicconcentrationof industriesis the resultof
The firstrow of table 7 repeatsthe averageresultsfrom
a
dynamic
processin whichthe combinationof plantbirths,
table 6. The second and thirdrows look separatelyat the
and
act togetherto mainclosures,
expansions/contractions
most geographicallyconcentratedone-thirdand the least
tain
a
level
of
industrial
concentration.Exslow-changing
geographicallyconcentratedone-third of industries (in
theories
of
industrial
location
have
dynamic,as well
termsof 1972 valuesof the EG index).Ourmainconclusion isting
as
and
that
data
on
the dynamics of
static, implications,
here is thatthe full sampleresultsare also representativeof
locations
can
offer
valuable
information
about the
what has happenedwithin the highly geographicallycon- plant
relevance
of
different
theories.
centratedindustries.In the nonlocalizedindustries,new firm
births and expansions have not had a deagglomerating One of ourmorestrikingfindingsis thatmanygeographeffect, and levels of geographic concentrationhave in- ically concentratedindustriesdo not exhibit any less moindustry.Althoughhiscreased(albeitonly slightlygiven thatthe base to whichthe bility thana typicalunconcentrated
torical
accidents
stressed
Arthur
(as
(1986) andKrugman
by
is
percentagesapply very small.)
The finalfour rows of the table describethe behaviorof (1991a)) may have long-lastingeffects in the textile industhe same four subsamplesof the set of highly geographi- tries,they arenot so importantin high technologyandmany
cally concentratedindustriesthatwe discussedin subsection otherindustries.We regardthe stabilityof geographicconIVB in connectionwith table3. The life cycle patternof the centrationdespiteindustrymobilityas strongevidencethat
locationof the high-techindustriesdiffers somewhatfrom levels of geographicconcentrationare determinedby funthe overall pattern:both the openings of new plants by damentalindustrycharacteristics.
A second findingis that new plant birthstend to act to
existing firmsand the net expansionsthathave occurredin
reduce
have
had
geographicconcentration.The benefitsfromwithinexisting plants
strongerdeagglomeratingeffects
in
than
the
There
here
also seems, how- industryspillovers on new plant formationapparentlydo
averageindustry.
to
ever, havebeen a greaterdifferencebetweenplantclosure not have a sufficientlystrongeffect to maintainconcentraratesin andawayfromindustrycenters,so, in the aggregate, tion levels by themselves.The dispersionof new plantsis
geographicconcentrationin these industrieshas decreased perhapsmorein line with the Jacobsview of the importance
of diversefactorsin generatingnew businesses,butexisting
only a bit more thanin the typicalindustry.
have really not focused on the effects of externaltheories
The textile and apparelindustriesstand out for having
ities
at
different
become more geographicallyconcentratedover the last
stages of a plant'slife and do not account
well
for
our
view of the plantclosureprocessas maintaining
twenty years.The largestpartof this differenceis attributable to net expansionsacting to reinforcegeographiccon- concentration.
These patternsare just the broadestregularitiesin our
centration,with plant births (to new and old firms) also
having less of a deagglomeratingeffect than in the full data.As we've noted, there are many differentpatternsin
different industriesand in different time periods-some
sample.
FORVARIOUSSUBSETSOF INDUSTRIES
TABLE7.-LIFE CYCLEDECOMPOSmTONS
Set of Industries
Full sample
Geographicallyconcentrated
Geographicallyunconcentrated
Concentratedhigh technology
Concentratednaturalresource
Concentratedtextile & apparel
Concentratedcrafts
Average PercentageAveragePercentage
New Firm Births
Change in /,
-3.2
-2.2
4.9
-4.1
-8.3
0.9
-0.1
-2.5
-3.1
-0.0
-1.8
-3.2
-1.5
-4.3
PercentageChange in ~, Attributedto:
Old Firm Births
Closures
-0.9
-1.3
1.6
-2.7
-0.7
0.3
-0.7
1.5
2.5
1.3
5.1
0.4
0.4
2.5
Expansions/Contractions
Switches
-2.2
-2.6
0.4
-5.6
-3.9
0.5
-1.6
The table provides decompositions of percentagechanges in geographic concentrationinto portions attributableto events at various stages of the plant life cycle for different subsets of industries.
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1.0
1.2
2.4
0.8
0.8
1.9
3.0
GEOGRAPHICCONCENTRATIONAS A DYNAMIC PROCESS
203
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1991a).
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researchbothon the traditional
,"IncreasingReturns and Economic Geography,"Journal of
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An obvious topic for future empirical research is to
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CEPRdiscussionpaperno.
Specialization,"
1230 (1995).
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(1999), 209-251.
they have differentpredictionsfor which industrieswill be Marshall,Alfred,Principlesof Economics(London:Macmillan,1920).
coagglomerated,which areas that are not now industry Maurel,Francoise,and BeatriceSedillot,"A Measureof the Geographic
Concentration
in FrenchManufacturing
Industries,"RegionalScicenterswill be fertile areasfor new firmbirths,and so on.
ence and UrbanEconomics29:5 (1999), 575-604.
We are exploringthese ideas in ongoing work.
McGuckin,Robert,and GeorgeA. Pascoe, Jr., "The LongitudinalResearch Database:Status and ResearchPossibilities,"Survey of
CurrentBusiness68:11 (1988), 30-37.
REFERENCES
Establishments
McGuckin,Robert,and SuzannePeck, "Manufacturing
LocationPatternsandthe Importanceof History,"
Reclassifiedinto New Industries:The Effect of Survey Design
Arthur,Brian,"Industry
CEPRdiscussionpaperno. 84, StanfordUniversity,(1986).
Rules,"Journalof EconomicandSocialMeasurement19:2(1993),
121-139.
Beardsell, Mark, and J. VernonHenderson,"SpatialEvolution of the
ComputerIndustryin the USA,"EuropeanEconomicReview43:2
(1999), 431-456.
APPENDIX
Davis, Steven, and John Haltiwanger,"GrossJob Creation,Gross Job
Destructionand EmploymentReallocation,"QuarterlyJournalof
In this appendix,we providea more completederivationof the life
Economics107:3 (1992), 819-863.
Davis, Steven, John Haltiwanger,and Scott Schuh, Job Creationand cycle decompositionof changesin the averageplantHerfindahl.
Let eik, be the employmentlevel in the kth plantin industryi at time
Destruction(Cambridge,MA: The MIT Press, 1996).
1
Dumais,Guy, GlennEllison, and EdwardL. Glaeser,"GeographicConeiktl/k
eikt, AZikt
Zikt+l
Zikt, and zi Zikt -i
centrationas a DynamicProcess,"NBER workingpaperno. 6270 t. Define zik,
N
(1997).
where Ni is the numberof plantsthat operatein the industryeither in
Dunne,Timothy,MarkRoberts,and LarrySamuelson,"TheGrowthand period t or in period t + 1.
Failureof Manufacturing
Plantsin the U.S.," QuarterlyJournalof
If one runsa regressionwith employmentchangeswithineach plantEconomics104:4 (1989a), 671-698.
that
industryas the dependentvariableon the sampleof plant-industries
"Plant
and
Turnover
Gross
Flows
in
the
U.S.
,
Employment
have positive employmenteitherin periodt or periodt + 1
Sector,"Journalof LaborEconomics7:1 (1989b),
Manufacturing
48-71.
Zikt = ai + Zikt +
Zikt+l
ikt,
(Al)
Ellison, Glenn, and EdwardL. Glaeser,"GeographicConcentrationin
U.S. Manufacturing
Industries:A Dartboard
Approach,"Journalof theestimateswill
alwayssatisfyd = 0, Zik, = 0, andZk Zak^ik= 0. (Note
Political Economy105:5 (1997), 889-927.
thatwe
"plant-industry"
just to indicatethatthere'sone observationon
, "TheGeographicConcentrationof Industry:Does NaturalAd- each sayfor
eachindustryto whichit belongsin eithertimeperiodof the
plant
American
Economic
Review
89:2
vantageExplainAgglomeration,"
pair;a plantthathas switchedindustriesbetweent and t + 1 thus has its
(1999), 311-316.
in the regression.)
andIndustrialOrganization, experiencesrecordedin two observations
Enright,Michael,GeographicConcentration
Changesin H, are relatedto the regressioncoefficientsby
unpublisheddoctoraldissertation,HarvardUniversity(1990).
Florence,P. Sargant,Investment,Locationand Size of Plant (London:
CambridgeUniversityPress, 1948).
+
H,+ -H = (2P + 2) Ht S kt
in the US Since
Fuchs,Victor,Changesin the Locationof Manufacturing
1929 (New Haven:Yale UniversityPress, 1962).
2
i
Glaeser,EdwardL., Hedi D. Kallal,Jose Scheinkman,andAndreiShlei= H,
fer, "Growthin Cities," Journal of Political Economy 100:6 To see this, we simply note thatZk zi2k = Zk Zikt -N) N
Hi
Ni
(1992), 1126-1152.
andthensubstitute
theregressionequationintotheplantHerfindahl
formula:
Henderson,J. Vernon,UrbanDevelopment:Theory,Fact and Illusion
(New York:OxfordUniversityPress, 1988).
-2
Z-2
7-lE
Henderson,J. Vernon,Ari Kuncoro,and MattTurner,"IndustrialDevel- H, =
H,+I 1tlH
ikt+1 ik
opment of Cities,"Journal of Political Economy 103:5 (1995),
1067-1090.
Holmes, Thomas,"How IndustriesMigratewhen AgglomerationExter=
+ AZ,kt
2Aikikt
nalitiesare Important,"
Journalof UrbanEconomics45:2 (1999),
ik
240-263.
Hoover,E. M., TheLocationof EconomicActivity(New York:McGraw
1
=
+ E,ik)Zikt + (tik,, + jik,)
Hill, 1948).
I7 ik 2(P~zi
Kim, Sukkoo,"Expansionof Marketsandthe GeographicDistributionof
EconomicActivities:The Trendsin U.S. RegionalManufacturing
'
compatible with many theories and some seemingly at odds
with much of what has been written. In recent years, authors
have tried to model the dynamics of agglomerationas well as
=
20 Krugmanand Venables(1995), Holmes (1999), and
Krugman,Fujita,
and Mori (1999) are notableexamplesof explicitlydynamicmodels.
(2P + 82)
ik
Z-i2k
E
+-
ik
2) 1 e1N
(2b + 8')
=
ik \
Ilik
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All use subject to JSTOR Terms and Conditions
i2,
2
i
Ni+ -Iik ik.
204
THE REVIEW OF ECONOMICS AND STATISTICS
Let
Aeikt - ZiktAEit
that the AH' defined in equation (4) in the text satisfy Ht+1 - H, = Ej
AH' then follows immediatelyfrom the expressionfor H,t+ - Ht given
previously.
Again, the definitioncan be motivatedby regardingthe formulaas
attributingto events in the jth categoryboth the change in the plant
If we estimate separateregressionsfor each of the J componentsof Herfindahlthat would have resultedif those events were the only employmentchangesanda portionof the additionalchangein the Herfindahl
changesin the plant-industry
employmentshares,
thatresultsfromthe correlationbetweeneventsof thejth andothertypes.
In thinkingaboutcorrelationhere (andif one wantsto thinkaboutmean
+
+
Az^=^4-p^4-?^
AZlk,
Eikt,
f3jZikt
atj
reversionand randomness),it is importantto keep in mind that the
the estimateswill be relatedto the estimatesobtainedfromthe regression relevantcorrelationshere are only those at the level of the individual
(Al) of overall share changes by S = 2ij ij and eikt = ;j Vkt- The fact plant.
AZ kt =
Eit+ I
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All use subject to JSTOR Terms and Conditions