Session 2: Agglomeration Forces - Princeton Universityerossi/Urban/CAF/Session2.pdf · S.S....

Session 2: Agglomeration ForcesTopics in Urban Economics, CAF

Esteban Rossi-Hansberg

Princeton University

ERH (Princeton University ) Session 2: Agglomeration Forces 1 / 27

The Need for Agglomeration Forces

Discussion based on Duranton and Puga (2004)

Agglomeration Economies needed to explain why economic activity is soconcentrated

I In 1992 only 1.9% of land in the US was built-up or pavedI Almost all new development is less than a km away from earlier developmentI Form of localized increasing returns

Hard to explain just using land heterogeneity (e.g. Chicago and LakeMichigan)

Spatial Impossibility Theorem (Starrett, 1978)I Homogenous space and the absence of indivisibilities or increasing returnsleads to autarchic locations


Sprawl

A Portrait From Space

�is map reproduces data from the paper “Causes of Sprawl: A Portrait from Space”, by Marcy Burchfield, Henry G. Overman, Diego Puga, and Matthew A. Turner, Quarterly Journal of Economics (), May . �e underlying data records the preponderant land cover in each of . billion × metre squares on a regular grid covering the continental United States. land cover ( urban land, land not developed, and water) is based on National Land Cover Data from the United States Geological Survey, derived mainly from Landsat �ematic Mapper satellite imagery. Urban land circa is a subset of urban land identified on the basis of s Land Use / Land Cover Data from the United States Geological Survey, derived mainly from high-altitude aerial photographs. Urban development – is urban land not in urban use circa .

© Marcy Burchfield, Henry G. Overman, Diego Puga, and Matthew A. Turner.

Non-urban land

Water

Urban land circa

Urban land built –

Scale: : ,,

Albers Equal Area Projection

Kilometres

Statute Miles


Classification

Classic classification (Marshall, 1890)I Labour-market interactionsI Linkages between intermediate and final good suppliersI Knowledge spillovers

Puga and Duranton’s classificationI Sharing

F Indivisible facilities, suppliers, customers, risk

I MatchingF Improved matching of labor or firms, higher probability of matching (hold-upproblems)

I LearningF Generation, diffusion and accumulation of knowledge


Sharing

Example of an Opera House or a Sports Arena

Large indivisibility generates increasing returns because extra unit of thegoods is provided at a lower average cost

I Factory town with large plant is also an exampleI So present both on the consumption and production sides

However, it does not solve the issue of why we see many of these facilities inthe same city


Sharing the Gains from VarietyAssume output in a particular sector is built out of intermediate goodsthrough a constant elasticity of substitution function

Y =[∫ n0(x (h))1/(1+ε) dh

]1+ε

where (1+ ε) /ε is the elasticity of substitution and n is the number ofvarieties.

The quantity of each variety is given by

x (h) = βl (h)− α

where α denotes a fixed cost and β is the MPL

After some normalizations leads to

Y = L1+ε

So an increase in final production by virtue of sharing a wider variety ofintermediate suppliers requires a less-than-proportional increase in primaryfactorsERH (Princeton University ) Session 2: Agglomeration Forces 6 / 27

Leads to Cities that Are Too Large

G. Duranton anld D. Puga

distribution of workers, any equilibrium must be characterised by full specialisation ofeach and every city in a single sector.

2.2.4. Equilibrium city sizes

We now turn to calculating equilibrium city sizes. Consider how the utility of individualworkers in a city varies with the city's population. With free trade in final goods andhomothetic preferences, utility is an increasing function of consumption expenditure. Inequilibrium, all workers receive the same consumption expenditure because the length-ier commuting for those living further away from the CBD is exactly offset by lowerland rents. Substituting the expression for net labour of Equation (9) into the aggregateproduction function of Equation (7), dividing by Ni, and using the urban specialisationresult yields consumption expenditure for each worker as

ci= (N T(.- (1)N) + (II)

Note that land rents do not appear in this expression because each worker receives anincome from her share of local land rents equal to the rent of the average local worker.While individual land rents differ from the average, lower rents for those living furtheraway from the CBD are exactly offset by lengthier commuting.

As shown in Figure 1, utility is a single-peaked function of city size which reachesits maximum for population

N j *= - 2 (12)(1 + 26J)r

Utility

PopulationSmall Large

City Size City Size(Unstable) (Stable)

Figure I. Utility as a function of city size.

2074

Problem is coordination failure

Everyone is too small to start a city at the effi cient size

Only at very large city sizes do individuals have an individual incentive tostart new cities


Other Ways of Sharing

Sharing gains from specializationI Smith’s famous "pin factory" exampleI Having more workers increases output more than proportionately not becauseextra workers can carry new tasks but because it allows existing workers tospecialize on a narrower set of tasks

F Improved dexterity or "learning by doing"F Saves fixed costs of switching tasksF Fosters labor saving innovations

Sharing riskI A localized industry gains a great advantage from the fact that it offers aconstant market for skill


Matching

Matching externalities are common in the labor market:I An increase in the number of agents trying to match improves the expectedquality of each match

Good example is Salop (1979)I Firms locate in a circleI The more firms the closer consumers are to one of them, and so the lower thetransport costs they pay to buy

I Can be applied to a variety of contexts and leads to better quality of matches

Another approach uses random matching and leads to a higher frequency ofmatches

I Based on a matching function that depends on number of unemployed andvacancies

I Market tightness, the ratio, implies an externality


Learning

Learning in many cases requires face-to-face interactions

The learning opportunities offered by the cities could provide a strongjustification for their own existence

Three distinct channels:I Knowledge generation

F Agglomerations are good incubators of new firms: Silicon Valley, Route 128F Life cycle of firms starts many times in cities

I Knowledge diffusionI Knowledge accumulation

We saw an example of this mechanism in Lecture 1


Knowledge Diffusion

One example of technology diffusion commonly used is exemplified in thefollowing expression:

Y (s) =(∫

g(s, s ′

)b (Y (s)) ds ′

)F (l (s) , r (s))

where g (s, s ′) is the spatial discount function and b (Y (s)) is the density ofoutput.

The examples in Lucas and Rossi-Hansberg (2002) and Rossi-Hansberg(2004) reviewed in Lecture 1 use

Y (s) =(∫

e−δ‖s−s ′‖b (l (s)) ds ′)F (l (s) , r (s))

where ‖s − s ′‖ denotes the distance between s and s ′I So in this case the knowledge spillover is the result of interactions betweenpeople at work


Overview of Evidence

Discussion based on Rosenthal and Strange (2004)

75% of Americans in cities in 2% of the area

Individual industries are concentrated tooI True for industries that use particular raw materials as well as for otherindustries


Furniture

61

Figure 1: Furniture Employment (SIC 25) Per Square Mile Fourth Quarter 2002; Source: Dun and Bradstreet

Red: Greater than 10; Orange: 4 to 10; Dark Yellow: 2 to 3; Light Yellow: 1 to 2; Green: 0


Software

62

Figure 2: Existing and New Software Establishments in Silicon Valley Fourth Quarter 1997; Source: Dun and Bradstreet


Key Results

S.S. Rosenlthal and ¢WC. Strange

3. The sources of urban increasing returns

As noted earlier, there are many potential sources of agglomeration economies. A com-plete understanding of urban development clearly requires that these sources be under-stood. Some of these microfoundations were suggested by Marshall (1920), includingknowledge spillovers, labor market pooling, and input sharing. There are many othercauses of agglomeration that were not discussed by Marshall, including home marketeffects, urban consumption opportunities, and rent-seeking. The literature on the the-oretical microfoundations of agglomeration economies is surveyed in another chapter[Duranton and Puga (2004)]. This section will consider econometric evidence on micro-foundations. Table 2 provides an overview of some of the studies to be discussed. Three

Table 2The Marshallian microfoundations of agglomeration economies

Microfoundation Paper Key results

Natural advantageInput sharingLabor market pooling

Knowledge spillovers

Home market effects

Consumption

Rent seeking

Multiple

Kim (1999), Ellison and Glaeser (1999)Holmes (1999)Diamond and Simon (1990)Kahn and Costa (2001)

Jaffe, Trajtenberg and Henderson (1993)

Rauch (1993a), Moretti (2000)Davis and Weinstein (1999)

Tabuchi and Yoshida (2000)

Glaeser, Kolko and Saiz (2001)

Waldfogel (2003)

Ades and Glaeser (1995)Henderson (2003b)

Rosenthal and Strange (2001)

Dumais, Ellison and Glaeser (1997)

Audretsch and Feldman (1996)

Factor endowments matter

More purchased inputs in clusters

Labor market risk capitalized in wagesHigh-education married locate in largecities

More citations of a patent in the sameMSA, controlling for industry effectsCity average education raises wage

For some industries, regional develop-ment explained by market access

Real wages lower in cities (reflectingconsumption possibilities)Various measures of consumption pos-sibilities predict growthAgglomeration enhances consumptionpossibilities in radio listeningDictatorship predicts mega-citiesDictatorship encourages urban pri-macy, which discourages growthEvidence of labor market pooling atstate, county, and zipcode levels of ge-ography; of knowledge spillover andinput sharing at zipcode and statelevels

Strongest evidence for labor marketpooling, some evidence for knowledgespillovers and input sharingEvidence of input sharing and knowl-edge spillovers at the state level

2144


Duranton and Overman (2005)

Need a way to measure industrial concentration

What seems like industrial concentration might be misleading due to thesmall number of plants

I The law of large numbers does not apply

Ellison and Glaeser (1997) dartboard approachI E.g. 75% of the employees in the U.S. vacuum cleaner industry work in one offour main plants

I Even if these plants locate separately, four locations must account for at least75% of the employment in this industry without it being localized in anymeaningful way


Some Examples1082 REVIEW OF ECONOMIC STUDIES

(a) Basic Pharmaceuticals(SIC2441)

(b) Pharmaceutical Preparations(SIC2442)

(c) Other Agricultural and ForestryMachinery (SIC2932)

(d) Machinery for Textile, Apparel andLeather Production (SIC2954)

FIGURE 1

Maps of four illustrative industries

at Princeton University on A

pril 4, 2012http://restud.oxfordjournals.org/

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Characteristics of a Measure of Localization

Any test of localization should rely on a measure which:1 is comparable across industries;2 controls for the overall agglomeration of manufacturing;3 controls for industrial concentration;4 is unbiased with respect to scale and aggregation

Their measure considers the distribution of distances between pairs ofestablishments in an industry and compares it with that of hypotheticalindustries with the same number of establishments which are randomlydistributed conditional on the distribution of aggregate manufacturing


The Measure of Localization

Data selection: Sometimes cutting out the lower tail might be useful becauseestablishments do something else

Let dij denote the distance between establishments i and j then theK−density at distance d is given by

K (d) =1

n (n− 1) hn−1∑i=1

n

∑j=1+1

f(d − dijh

)where f is the Gaussian kernel, n is the number of establishments, and h isthe bandwidth.

Need to use a Kernel comes form the error in measuring "effective distance"

Note that the number and size of plants is taken as given


The Examples1084 REVIEW OF ECONOMIC STUDIES





0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

FIGURE 2

K -density, local confidence intervals and global confidence bands for four illustrative industries

the entire industry population. If, instead of a census, we had a random sample of firms from eachindustrywe would need to worry about the statistical variation due to the estimation of the actualK -density. Applications of the techniques developed below to samples of firms from particularindustries could allow for this statistical variation to be taken into account but the exhaustivenature of our data means that we are able to ignore it in what follows (seeEfron and Tibshirani,1993, andQuah,1997, for further discussion of these issues as well asDavison and Hinkley,1997, for a discussion more focused on point patterns).

Thesecond difference stems from the fact that the spatial nature of our data implies strongdependence between the bilateral distances that are used to calculate the density. This strongdependence arises because the observations of interest are actually the points that generatethese bilateral distances. Even if the underlying points are independently located, the bilateraldistances between these points will not be independent.6 This has implications for the samplingtheoryof our estimator,K A(d). In situations where the observations are independent (or only

6. See below for more on this issue.



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Counterfactuals

Still need to control for the overall tendency of manufacturing to agglomerate

Draw locations for plants in feasible "sites" and calculate the counterfactualdensity fixing the number of plants

I Sampling without replacement

Run many simulations and take the top 5% and lowest 5% in the generatedsample

The result is a confidence interval for what would happen if the industry wasrandomly located

When for industry A, KA(d) > KA(d), this industry is said to exhibitlocalization at distance d (at a 5% confidence level)

Symmetrically, when KA(d) < KA(d), this industry is said to exhibitdispersion at distance d (at a 5% confidence level)


The Index

Define an index of localization as

γA (d) ≡ max(KA(d)−KA(d), 0

)To reject the hypothesis of randomness at distance d because of localization(dispersion), we only need γA (d) > 0

Similarly the dispersion index is calculated as

ψA (d) ≡ max(KA(d)− KA(d), 0

)Similarly global measures are calculated when we use a bound determined bythe top 5% or realizations at any given distance


The Examples1084 REVIEW OF ECONOMIC STUDIES





0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

FIGURE 2

K -density, local confidence intervals and global confidence bands for four illustrative industries

the entire industry population. If, instead of a census, we had a random sample of firms from eachindustrywe would need to worry about the statistical variation due to the estimation of the actualK -density. Applications of the techniques developed below to samples of firms from particularindustries could allow for this statistical variation to be taken into account but the exhaustivenature of our data means that we are able to ignore it in what follows (seeEfron and Tibshirani,1993, andQuah,1997, for further discussion of these issues as well asDavison and Hinkley,1997, for a discussion more focused on point patterns).

Thesecond difference stems from the fact that the spatial nature of our data implies strongdependence between the bilateral distances that are used to calculate the density. This strongdependence arises because the observations of interest are actually the points that generatethese bilateral distances. Even if the underlying points are independently located, the bilateraldistances between these points will not be independent.6 This has implications for the samplingtheoryof our estimator,K A(d). In situations where the observations are independent (or only

6. See below for more on this issue.



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Findings Across Industries

1090 REVIEW OF ECONOMIC STUDIES

TABLE 1

Localizationat three thresholds for four-digit industries

Percentage of four-digit industries localized at:

5 km 5 km only 5 and 30 km only 5 and 150 km only 5, 30 and 150 km39·3 6·4 22·6 0·9 9·4

30 km 30 km only 30 and 150 km only38·9 6·0 0·9

150 km 150 km only17·1 6·0

(a) Global localization

100

90

80

70

60

50

40

30

20

10

00 20 40 60 80 100 120 140 160 180

Distance (km)

(b) Global dispersion

100

90

80

70

60

50

40

30

20

10

00 20 40 60 80 100 120 140 160 180

Distance (km)

(c) Local localization

100

90

80

70

60

50

40

30

20

10

00 20 40 60 80 100 120 140 160 180

Distance (km)

(d) Local dispersion

100

90

80

70

60

50

40

30

20

10

00 20 40 60 80 100 120 140 160 180

Distance (km)

FIGURE 3

Number of four-digit industries with local/global localization and dispersion

across distances, but not across the two figures.13 It is immediately apparent that the extent oflocalizationis much greater at small distances than large distances. As before, dispersion doesnot show any marked pattern. The important conclusion we draw here is that localization tendsto take place mostly at fairly small scales.

13. This is because for an industry that exhibits localization the density is unbounded from above whereas thedensityof an industry that exhibits dispersion is bounded from below by zero.



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Taking Intensity into AccountDURANTON & OVERMAN TESTING FOR LOCALIZATION 1091

(a) Global localization

0·240·220·200·180·160·140·120·100·080·060·040·020·00

0 20 40 60 80 100 120 140 160 180Distance (km)

(b) Global dispersion

0·240·220·200·180·160·140·120·100·080·060·040·020·00

0 20 40 60 80 100 120 140 160 180Distance (km)

FIGURE 4

Index of global localization and dispersion by distance

0·50

0·45

0·40

0·35

0·30

0·25

0·20

0·15

0·10

0·05

0·000 20 40 60 80 100120140160180200220240

FIGURE 5

Distribution of global localization and dispersion by four-digit industries

Differences between industries

We now turn to the examination of differences between industries. We start by constructinga measure of the extent to which different industries deviate from randomness. Proceedingas before, for each industryA we can define the following cross-distance indices:0A ≡∑180

d=00A(d), and9A ≡∑180

d=09A(d). Respectively, these measures are the sum for eachindustry of the index of global localization and dispersion across all levels of distance. Toillustrate the variations in industry outcomes, we rank industries by decreasing order of theseindices and plot them inFigure 5. The upper line is the measure of localization, the lower that ofdispersion.As is immediately clear, there are a few industries that show very high localization ordispersion, but the majority of industries do not see such extreme outcomes. This highly skeweddistribution of localization confirms previous findings (Ellison and Glaeser(1997),Maurel andSedillot (1999),Devereuxetal. (2004)).

To give some idea of the reality underlyingFigure 5,Table 2lists the 10 most localizedindustriesand the 10 most dispersed. Interestingly, more than a century afterMarshall(1890),Cutlery (SIC2861) is still amongst the most localized industries. Six textile or textile-related



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Particular Industries

1092 REVIEW OF ECONOMIC STUDIES

TABLE 2

Mostlocalized and most dispersed four-digit industries

SIC92 Industry 0 or9

Most localized

2214 Publishing of sound recordings 0·4701711 Preparation and spinning of cotton-type fibres 0·4112231 Reproduction of sound recordings 0·4031760 Manufacture of knitted and crocheted fabrics 0·3211713 Preparation and spinning of worsted-type fibres 0·3192861 Manufacture of cutlery 0·3141771 Manufacture of knitted and crocheted hosiery 0·2901810 Manufacture of leather clothes 0·2031822 Manufacture of other outerwear 0·1812211 Publishing of books 0·178

Most dispersed

1520 Processing and preserving of fish and fish products 0·2003511 Building and repairing of ships 0·1131581 Manufacture of bread, fresh pastry goods and cakes 0·0942010 Saw milling and planing of wood, impregnation of wood 0·0822932 Other agricultural and forestry machinery 0·0671551 Operation of dairies and cheese making 0·0641752 Manufacture of cordage, rope, twine and netting 0·0623615 Manufacture of mattresses 0·0501571 Manufacture of prepared feeds for farm animals 0·0492030 Manufacture of builders’ carpentry and joinery 0·047

industries are also in the same list together with three media-based industries. These highlylocalizedindustries are fairly exceptional. In contrast, the mean industry (after ranking industriesby their degree of localization) is barely more localized than if randomly distributed. It is mostlyfood-related industries together with industries with high transport costs or high dependence onnatural resources that show dispersion.

Our main focus in this paper is on the proportion of manufacturing sectors that are localized.However, it is interesting to notice that a number of industries that appear inTable 2are fairlysmall in terms of overall employment. This raises the question as to whether the percentage ofmanufacturing workers employed in localized industries is above or below the percentage ofsectors that are localized. Weighting sectors by their share in manufacturing employment, wefind that 67% of U.K. manufacturing employers work in sectors that are localized. This showsthat localized sectors tend to have a larger share of manufacturing employment. Offsetting this,however, is the fact that the employment share weighted mean of the index of globalization,0A, is 30% lower than the unweighted mean of the index. That is, larger sectors tend to be lessstrongly localized.

Finally, it is also interesting to notice that for many (two-digit) branches, related industrieswithin the same branch tend to follow similar patterns.Table 3 breaks down localizationof industries by branches. For instance nearly all Food and Drink industries (SIC15) orWood, Petroleum, and Mineral industries (SIC20, 23 and 26) are not localized. By contrast,most Textile, Publishing, Instrument and Appliances industries (SIC17–19, 22 and 30–33) arelocalized. The two main exceptions are Chemicals (SIC24) and Machinery (SIC29). In thesetwo branches, however, the more detailed patterns are telling. Chemical industries such asFertilisers (SIC2415) vertically linked to dispersed industries are also dispersed whereas thoselike Basic Pharmaceuticals (SIC2441) or Preparation of Recorded Media (SIC2465) verticallylinked to localized industries are themselves very localized. The same holds for machinery: Other



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Particular IndustriesDURANTON & OVERMAN TESTING FOR LOCALIZATION 1093

TABLE 3

Localizationby two-digit branch

Two-digit branch Number of No. global No. globalfour-digit localization localizationindustries ≤60 km >60 km

15 Food products and beverages 30 1 016 Tobacco products 1 1 017 Textiles 20 16 918 Wearing apparel, dressing, etc. 6 6 319 Tanning and dressing of leather, footwear 3 3 320 Wood and products of wood, etc. 6 0 021 Pulp, paper and paper products 7 2 122 Publishing, printing and recorded media 13 13 823 Coke, refined petroleum products 3 0 024 Chemical and chemical products 20 8 825 Rubber and plastic products 7 1 326 Other non-metallic mineral products 24 4 227 Basic metals 17 11 1028 Fabricated metal products 16 9 1229 Other machinery and equipment 20 6 930 Office machinery and computers 2 2 231 Electrical machinery 7 2 532 Radio, televisions and other appliances 3 3 333 Instruments 5 3 434 Motor vehicles, trailers, etc. 3 1 335 Other transport equipment 8 2 236 Furniture and other products 13 4 5

Aggregate 234 98 92

Agricultural and Forestry Machinery (SIC2932) is very dispersed like most agriculture-relatedindustries,whereas Machinery for Textile, Apparel and Leather Production (SIC2954) is verylocalized like most textile industries.

5. ESTABLISHMENT SIZE AND LOCALIZATION

Four main conclusions emerge so far: (i) 52% of industries are localized, (ii) localization mostlytakes place at small scales, (iii) deviations from randomness are very skewed across industriesand (iv) industries that belong to the same branch tend to have similar localization patterns. Thesefindings may be driven by particular types of establishments or particular sectoral definitions. Togain insights about the size of localized establishments and the scope of localization, we replicateour analysis with alternative samples of plants and alternative sectoral definitions. This sectiondeals with size issues; questions relating to scope are examined in the next section.

Note that the issue of size may be particularly crucial as firm-size distributions arevery skewed in most industries. In our population of plants, 36% of establishments employtwo persons or less and represent only a very small fraction (2·4%) of total manufacturingemployment. The issue of firm size is also important from a policy perspective. Policiesencouraging dispersion are not likely to be very successful if it is only small establishments thatcan be dispersed, whereas clustering policies might be more difficult to implement if it is onlylarge establishments that cluster. Finally, the type of establishments, big or small, that cluster ordisperse is potentially very informative about the relevance of particular theories.



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