Measures of concentration

1. Comparable across industries

2. Comparable across spatial scales

3. Unbiased with respect to arbitrary changes to spatial classification

4. Unbiased with respect to arbitrary changes to industrial classification

5. Carried out with respect to a well-established benchmark

6. Allow to determine whether significant differences exist between an observed distribution and its benchmark

Properties of an ideal index of concentration

Measures of concentration

• E = employment• s = ratio • i = sector i= 1,……., N• j = region j= 1,……., M• employment in sector i in region j

• total employment of region j • total employment of sector i

• total employment in the country

ijE

j iji

E E

i ijj

E E

iji j

E E

ijeij

j

Es

E i

iE

sE

Coefficient of specialization

eij

i

ss

Coefficient of specialization of region j in sector i

ijcij

i

Es

E j

j

Es

E

Localization coefficient (or Hoover-Balassa)

cij

j

ss

Coefficient of localization of sector i in region j

Herfindhal index

2

1

( )n

e ej ij

i

H s

11,n

12

ej ij i

i

IDEA s s

2

1

( )m

c ci ij

j

H s

11,m

12

ci ij j

j

IDCA s s

Index of Isard

0,1

0,1

The Gini Index

The most popular index for measuring inequalityHere we use it to evaluate the spatial concentration of a given sector in terms of employment

1

n

jj nj

S s

Cumulative percentage of js

11

1m

c ci j ij n ij n

n

G s S S

cijs js c

ij js s cijS jSRegion

1 0.1 0.2 0.5 0.1 0.2

2 0.2 0.25 0.8 0.3 0.45

3 0.3 0.25 1.2 0.6 0.7

4 0.4 0.3 1.3 1 1

1 ·1·1 0.52

ODCBAGODE

ODE

( )ODCBA ODE OAI ABGI BCFG CDEF

1 2 0.2 0.1OAI

1 2x(0.1+0.3)x(0.45-0.2)ABGI 1 2x(0.3+0.6)x(0.7-0.45)BCFG

1 2x(0.6+1)x(1-0.7)CDEF

0.5 0.4125 0.0875ODCBA

0.0875 0.1750.5

G

Index of Ellison y Glaeser• All previous indexes are sensitive to industrial and spatial definitions

• The EG index has into account the size distribution of the establishments of each industry and fulfills the first property

• Exemple of EG: 75% of employment in the vacuum-cleaner industry is covered by merely four plants in USA

• The reference of EG is the distribution of employment if all plants in a sector were located randomly

• Let be N the number of plants in a sector and the percentage of employment across the plants of the sector

1,..., ,...,l Nz z z

1lju

1lj jP u s

,lj kjcorr u u

The correlation between the location choices of two plants l and k belonging to the same sector is an index:

where If plant l in sector i is located in region j and 0lju otherwise

If 0 , location choices are independent, which corresponds to a randomdistribution of plants across space

If 1 , all plants in this sector are located together

If the distribution of economic activity is the benchmark, the probability that aa given plant in sector i chooses to be located in region j is given by the relative size of this region with respect to the overall level of economic activity

2

2 2

1ˆ

1

EG

jj c

EG EG ij j lj l

G Hs

G s s H zH

EVIDENCE ON NEW ECONOMIC GEOGRAPHY

S. Kim (1995) “Expansion of markets and the geographic distribution of economic activities: the trends in the US regional manufacturing structure, 1860-1987”

Analyzes the evolution of specization and concentration of manufacturing in the long term

- Externalities - H-O- Internal increasing returns

A DESCRIPTIVE MODEL

Integration of US economy starts in 1860 and is completed by 1940s: Transportation costs: 1860-1890

Railway: by 1890 most railroad lines had converted their tracksto a standard gauge of 4'8.5”Miles built 30626 to 166703

Telegraph: Miles 50000 to 19382000 Price convergence: - Goods market: second half of 19th century - Interest rate early 20th century - Wages mid 20th century   

Units of analysis: Spatial 9 Census divisions (internalize factor mobility and externalities) Industrial: 2 digits (21) (homogeneous technology and externalities)

1

nij ik

jki j k

E ESIE E

ij

iUSij

j

US

EEL EE

Specialization

Localization

Specialization. Average of bilateral indexes

Localization. Average of Hoover-Balassa

First: trend due to half of sectorsthat increase weightSecond: h-t sectors are no more concentrated than traditional sectors → ¿No externalities?

- Heckscher-Ohlin (Resources y raw materials)- Internal returns to scale

Avarage number of workers per establishment Cost of raw materials/ Value added

0 1 2Location PlantSize RawMatIntensityit it it i t it

Elasticities: Plant size 0.157 Raw material intensity 0.223

- Historical trends in U. S. regional specialization can be explained jointly by models based on scale economies and resources.

- As transportation costs fell between 1860 and the turn ofthe twentieth century, firms adopted large-scale production methodsthat were intensive in relatively immobile resources and energysources. - The rise in scale and the use of immobile resources caused regions to become more specialized.

- As factors became increasingly more mobile and as technological innovations favored the development of substitutes, recycling, and less resource-intensive methods over the twentieth century, regional resource differences diminished.- The growing similarity of regional factor endowments and the fall in scale economies caused regions to become despecialized between World War II and today.

A STRUCTURAL MODEL

Accessibility to markets and firm’s profit: a framework for the empirical analysis

( )1rs

rs r rs

rsr rs r

qp m q m

1 1rs r rrs r rs rs rp p p m p m

( 1)rs r rs s s sq p Y P

1( 1) ( 1)( )

rs r rsrP n p

rp mill price rs iceberg transport cost rm marginal cost

elasticity of substitution/price elasticity rsq quantity sold by the firm in s

In the short-term with a given number of firms:

( 1)r rs r r r r

s

F cm RMP F Total profits of r over all markets

)1()1( c

s sssrsr PYRMP 1where is the Real Market Potential

1rsrs

freeness of trade

s sssrsr PYRMP 1 recall sr

s rs

YMPd

Market potential and factors attraction(Head y Mayer, 2004) Location decision of firms between two locations i and j depends on → Carlton (1983) logit model Hypothesis: firms locate where markets accessibility is highest Sample de 452 Japanese branch plants localized in 57 regions from 9 EU countries in the period 1984-1995

ji

1ln ln( ) ln ( 1) ln1r

r r rFU m RMP

rrrr Awm lnln)1(lnln

Variable costs: wages ¨rw price of other inputs (land, intermediates) r

rA Total factor productivity

1ln (1 ) ln ln ( 1) lnr r r r rU w A RMP

irrrrr RMPAwU ln)1(lnln)1(ln~ 1

expexp

rr

ss

UPU

Construction of the market potential:

s sssrsr PYRMP 1

Problem: we do not have data of rs and sP

We need to proxy these two variables: we will do it with trade flows

Trade flows estimated with a gravity equation:

( 1)rs rs s s sq p P Y

1 1RS R RS RS R R RS S S S

Market potential

X n q p n p Y P

SRSRRS FMFXX lnln

)ln( 1 RRR pnFX

)ln( 1SSSS YPFM

Supply capacity of export country

Market capacity of the import country

RSRSRSSRSRS FRLFRd lnln

Distance, border effect , same language

RSRSRSSRSSRRS FRLFRdFMFXX lnln

RRX National production minus exports

ˆ

ˆ

ˆˆ

ˆ ˆ ˆexp( )

ˆ

2ˆ3

rs S RS rs

rs rs

rrr rr

L d

d

Superfd

Regions from different countries

Regions from the same country

Intra-regional trade

)ˆexp()/(ˆˆ 1SSssss MFYYPY

Ss YY / Share of GDP of s on national GDP of country S

Potential built for 18 sectors (2 digits) each year

Production costs: 1. Labor costs observable (payroll sector /number of employees in the region) additionally: non labor costs (only vary across countries) Unemployment rate 2. Other costs non observable a. Capital cost affected by subsidies/taxes:- Corporate tax rate (only vary across countries)- Elegibility to benefit from Structural Funds (Objective 1) b. Control for land supply and price: - Area of the region        

Evidence on clusters. 3 types: - Number of establishments in the two-digit industry region- Number of Japanese affiliates in the three-digit industry region - Number of affiliates owned by the same Japanese parent or members of same vertical keiretsu

Possible efects of these clusters: - Lowering intermediates prices regional production networks- Share knowledge (non observable)- Clusters will form around the same exogenous sources of lowinput costs or high productivity Hypothesis: clusters form in areas with high market potential in the relevant industry  The hypothesis would receive support if after controlling for market potential,the presence of same industry firms lowers the attractiveness ofa region

A

Main results: Ambiguous with respect to RMP: - of RMP increases the probability of locating in the region in 3%-11%- “theory doesn’t pay”- Agglomeration variables the most important but, omitted variables?

10%

ECONOMIES OF AGGLOMERATION

ECONOMIES OF AGGLOMERATION

Density generates costs Higher cost of land Greater congestion, higher commuting and transport costs

Population and economic activity are ever more concentrated in cities

There must be offsetting benefits Higher productivity for firms Higher wages for workers

Are these advantages due to agglomeration economies?

What are their scale and scope and causes?

Why is it profitable for firms to concentrate employment?

1. Plant-level economies of scale Plants produce more efficiently at a larger scale

2. Agglomeration economies Plants produce more efficiently when close to other plants

A. Urbanization economieswhen close to other plants in general

B. Localization economieswhen close to other plants in the same industry

• Economies of agglomeration are externalities

• A person who is making an economic decision, such as whether to produce more output, makes the decision on the basis of his own marginal costs and benefits, and ignores costs or benefits that affect others

An example

• An industry in an urban area: demand, D and supply, S

• Made up of a large number of small, competitive firms

• Each of these firms has a lon-run average cost curve that has a minimum point at some level of output

• In the long run the output of the industry expands by adding more firms

• The long-run supply curve of the industry is the horizontal line S

•The market price is set equal to long-run average and marginal curve

Economy external to the firm but internal to the industry:

The expansion of the industry output, through the addition of another firm, will lower the average costs for the other firms

The price at which the firms in the industry will offer the good now drops tothe lower average cost

MICRO-FOUNDATIONS OF AGGLOMERATION ECONOMIES

• Sharing. • Matching.

• Learning.

1. SHARING

A. Sharing indivisible facilities

Simplest argument to justify the existence of a city Example: ice hockey rink

• Expensive facility with substantial fixed costs• Few individuals would hold a rink for themselves• An ice hockey rink is a an indivisible facility that can be shared by

many users Factory towns

B. Sharing the gains form the wider variety of input suppliers that can be sustained by a larger final goods industry

C. Sharing the gains from the narrower specialisation that can be sustained with larger production

Example: Dresses and Buttons

Some competing firms locate close to one another to share a firm that supplies an intermediate input (something one firm produces that a second firm uses as an input in its production process)

Buttons produced by one firm are used by a dressmaking firm

Production of high-fashion dresses

Demand for dresses subject to the whims of fashion dressmaking firms must be small and nimble (ready to respond quickly to changes in fashion)

Varying demand for dresses causes varying demands for intermediate inputs (e.g., buttons)

Demand for buttons changes from month to month Important → not in the quantity demanded, but in the type of buttons demanded(e.g., one month square blue buttons with a smooth finish and the next month round pink buttons with a rough finish)

Production of dresses is subject to constant returns to scale

Production of buttons

Subject to economies of scale. Use of indivisible inputs and specialized labour → Cost per button decreases as the quantity increases Scale economies large relative to button demand of individual dressmaker

Face time. A button for a high-fashion dress is not a standardized input. Requires interaction between dressmaker and button-maker Dressmaker must be located close to the button-maker

Modification cost. The dressmaker may incur a cost to modify the button to make a perfect match (e.g., to shave the edges of a square button to make it a hexagon)

Average cost of buttons from the perspective of the dressmaker

• Point a → High cost for an isolated dressmaker

Two reasons: - Low production of buttons - Button-maker produces only one type of button

• Point f → Low cost for the each dressmaker in a cluster Two reasons: - Sufficient demand for buttons to exploit economies of scale - Larger demand for buttons allow specialization of button-makers

Other example:

High-technology firms

- Rapidly changing demand → Small innovative firms

- Share suppliers of intermediate inputs (electronic components)

- Not standardized inputs → Face time

Model of gains from diversity

m 1,...,j m

1 j

j

11

10

jj

jnj jY x h dh

productive advantages of sharing a wider variety of differentiatedintermediate inputs produced by a monopolistically competitive industry ↓

Aggregate returns to scale  

There are  sectors

In each sector, perfectly competitive firms produce goods for final consumption under constant returns to scale

They use intermediate inputs, which are specific to each sector and enter into

plants’ technology with a constant elasticity of substitution

The higher the lower the elasticity of substitution

0j

Intermediates produced in monopolistic competititon Production is expalined by:

jjjj hlhx )()( Increasing returns

is the marginal productivity of labor is a fixed cost

1 jj j

jq w

Profit maximizing price

0 Long-term equilibrium

x

)1(

lxl

Number of firms in equilibrium: LlLn

)1(

Applying normalizations:

1

1

1

1( ) ( )

j

j jj j j jY n x L

An increase in final production by virtue of sharing a widervariety of intermediate suppliers requires a less than proportionalincrease in primary factors

Gains from specialization

Consider a perfectly competitive industry in which firms produce a final good by combining a variety of tasks that enter into their technology with a

constant elasticity of substitution 1

The number of tasks is fixed 0,h n

111

0

nY x h dh

Each atomistic worker is endowed with one unit of labour. Any worker allocating an amount of time l(h) to perform task h produces

Parameter of productivity Intensity of the gains from specialization

Note that l(h) can be interpreted as a measure of specialisation,since the more time that is allocated to task h the less time that is left for other tasks.

L workers and n tasks each worker devotes of her unit labour Ln

nL

to each of the she performs Ll hn

1Y n L

D. Sharing risk: labour pooling

Firms are subject to demand shocks

In each time period the demand for some firms grows and the demand for some other firms decreases

Unsuccessful firms will be firing workers at the same time that successful firms are hiring them

An agglomeration of firms facilitates the transfer of workers from unsuccessful firms to successful ones

The process occurs at the level of the firm, not the industry

A simple model

The total demand at the industry level is constant, but the demand for each firm varies from year to year

For each firm there are two possibilities equally likely: a. High demandb. Low demand

Isolated firm

A firm can be isolated The isolated firm doesn’t face any competition for labour within its town Labour supply is perfectly inelastic, fixed at 12 workers

High demand for the product of the firm ↓ High demand for labour

Equilibrium at point b → wage= $16

Low demand for the product of the firm ↓ Low demand for labour

Equilibrium at point h → wage= $4

Firm in agglomeration

Firms in agglomeration face competition for labour (labour supply perfectly elastic, horizontal line)

For every successful firm hiring workers, there is an unsuccessful firm firing them

Total demand for labour in the agglomeration is constant

A firm can hire as many workers as it wants at the market wage

High demand for labour ↓Firm hires 21 workers (point d)

Low demand for labour ↓Firm hires only 3 workers (point j)

Spatial equilibrium

Wage uncertain at the isolated site high demand w=$16, low demand w=$4 The two outcomes are equally likely: Expected wage (isolated firm) = 0.5 · $16 + 0.5· $4 = $10

To make workers indifferent between isolated site and agglomeration → w(agglomeration) = $10

Firm gains from agglomeration

Expected profits will be higher in the agglomeration Let’s suppose a firm moves from isolated site to agglomeration and then

experiences one year of high demand followed by a year of low demand

Good news when demand is high (w=$10 instead of w=$16, and can hire 21 workers instead of 12 workers)

Higher profitBad news when demand is low (w= $10 instead of w=$4) Lower profit

Which is larger, the good news or the bad news?– Good news dominate because a firm in the agglomeration responds to

changes in the demand for its product– Expected profit in agglomeration > Expected profit in isolated site (0.5 · adf) + (0.5· gjf) > (0.5 · abc) + (0.5 + ghi)

(0.5 · $147) + (0.5 · $3) > (0.5 · $48) + (0.5 + $48) $75 > $48

2. MATCHING. A. Improving the quality of matches between employers and

employees

Usual assumption → workers and firms are matched perfectly Each firm can hire workers with the skills the firm requires

In real world workers and firms are not always perfectly matched Mismatches require costly worker training

A large city can improve the matching of workers and firms in the real world

A simple model

Assumptions

Each worker has a unique skill described by a position or “address” on a circle with a one-unit circumference

There are 4 workers and skills evenly spaced on the circle The address of a worker is the distance between her skill position and the “north pole” of the circle Each firm enters the market by picking a product to produce and an associated skill requirement. S=1/8 S=5/8 Training costs. Workers incurs the cost associated to mismatch

0,2 8,4 8,6 8

Competition for workers. Each firm offers a wage to any worker who meets its skill requirement Each worker accepts the offer with the highest net wage net wage = wage offered by the firm - training costs

Each firm will hire two workers

Equilibrium

Each firm is the single employer in the skill interval surrounding its skill requirement Equilibrium with 4 workers (skill types) and 2 firms Equilibrium mismatch is 1/8 (workers at 0 and 2/8 work in firm

at 1/8, so each worker has a skills gap of 1/8)

Each firm pays a gross wage equal to the value of output produced by a perfectly matched worker. Net wage = Gross wage – Skills gap·Unit training costNet wage = $12 – 1/8 · $24 = $9

Introducing agglomeration

We represent an increase in the size of the labour force by increasing the number of workers on the unit circle

Now we have 6 workers (skill types) and 3 firms enter the market 0,2 12,4 12,6 12,8 12,10 12 1 12,5 12,9 12

Each worker has a mismatch of 1/12

Workers incur lower training cost

Net wage increases

Net wage = $12 – 1/12 · $24 = $10

An increase in the number of workers decreases mismatches and training costs

The presence of a large number of workers attracts firms that compete for workers, generating better skill matches and higher net wages This is an incentive for workers to live in large numbers in cities, so the attraction between frims and workers is mutual

3. LEARNING

The Obligatory Marshall Quotation

When an industry has thus chosen a locality for itself, it islikely to stay there long: so great are the advantages whichpeople following the same skilled trade get from nearneighbourhood to one another. The mysteries of the tradebecome no mysteries; but are as it were in the air, andchildren learn many of them unconsciously. Good work is rightlyappreciated, inventions and improvements in machinery, inprocesses and the general organization of the business have theirmerits promptly discussed: if one man starts a new idea, it istaken up by others and combined with suggestions of their own;and thus it becomes the source of further new ideas.

Alfred Marshall. 1890. Principles of Economics. London: Macmillan. Book IV,Ch. X, § 3: The advantages of localized industries; hereditary skill.

Cost and output for an industry Dynamic agglomeration economies

, ,Q A z t f K L

Three Types of Externalities (Glaeser et al. 1992)

1. Marshall-Arrow-Romer Local knowledge spillovers between firms in the same industry Specialization and concentration promote growth

Local monopoly helps growth by internalizing externalities

2. Porter Innovation in competitive industry clusters with many small firms Specialization and fragmentation promote city growth

Local competition requires firms to innovate or die

3. Jacobs Local knowledge transfers across industries

Diversification and fragmentation promote city growth “Cross-fertilization” of ideas across different lines of work

Evidence not conclusive

Glaeser et al. (1992) find evidence of Jacobs externalities explain the employment growth of sector-city

Henderson et al (1995) find that new industries appear in diverse cities but mature industries grow in specialized cities.

1,1,11 ·/log/log/log ttnactnactttt egAAwwll

)( ttt lfAQ

·t local nationalA A A

tnactnactlocaltlocaltt AAAAAA ,1,,1,1 /log/log/log

, 1 , 1log / , ,local t local t tA A g specialization monopoly diversity e

Nursery cities (Duranton and Puga, 2001)

Consider a firm that is looking for the ideal production process for a new product

By experimenting with different processes, the firm will find the ideal process

Once found the ideal process, the firm will switch to mass production and start earning a profit

Question is: where should the firm experiment, in a diverse city or a specialized city?

Cost and Benefits of both options (model)

First option → experiment in a diverse city and then move to a specialized city after discovering the ideal process

An experiment entails producing a prototype of the firm’s new product with a particular production process

Suppose there are six processes in the diverse city Once the prototype from the ideal process is finished, the firm will

immediately recognize that it has discovered the ideal process Assume that it takes on average three years Once discovered the ideal, the entrepreneur will move to a specialized

city and start making profits

• Cost of each prototype = $4 (losses of the firm each year of the 3 year)• Year 4 the firm moves to specialized city. Moving cost = $7• Assume firm operates 6 years • Last 3 years the firm earns a gross profit = $12• Firm’s lifetime profit is Net profit = Gross profit – Prototype cost – Moving cost Net profit = $36 – $12 – $7 = $17

Second option → search for the process in the specialized city

Advantage → lower prototype cost Each specialized city has the specialized inputs for one production

process Suppose, prototype cost = $3 · 3 years = $9

Disadvantage → Higher moving cost The search for the ideal process would require moves from one

specialized city to another An average of three moves, moving costs = $7 · 3 years = $21

Net profit = $36 - $9 - $21 = $6

Profit is lower when experimenting in specialized cities Different roles of diverse and specialized cities

Establishment relocations in France, 1993-1996

Combes et al. (2005)

Wage curve: wage as a function of the local labour force, w(N), is increasing in the size of the labour force reflecting agglomeration economies

Cost of living curve: commuting, housingand other consumption goods

Labour supply curve: indicates for any level of net wage, the amount of laboursupplied in the area (here it is assumedperfect mobility)

DIVERSITY, SPECIALIZATION AND URBAN SIZE

Cities of different size and productive specialization can be found in all the economies

Specialized and diversified cities co-exist

Medium size cities tend to be highly specialized in their production patterns, in terms of goods exported form the city

All cities have a base of locally produced goods and services just for local consumption: housing, retail and personal services, business services, repairs and education and health services. (about 60% of total employment)

• Two industries of similar size nationally (USA, 1987): Traditional textile (excluding apparel) High-tech instruments

Textiles Most metro areas have no employmentNone of metro areas > 1m even have 1% of employment in textileMost of specialized areas are medium-small

Instruments: Most metro areas have no employmentVery large metro areas record small sharesSome areas >1m. record shares that are almost 4% of local employment

Model

Firms, in each sector, require both sector-specific inputs as well as business services for their headquarters

There are agglomeration economies in all sectors

Firms face a trade-off between spatial integration of both headquarters and production facilities and the spatial separation of these two functions

If firms decide to split, then both parts of the operation can fully benefit from the relevant agglomeration economies: Sector specific inputs for production Business services for headquarters

Spatial integration Firms manage the interaction between production facilities and headquarters more

efficiently because of savings on communication costs But more expensive inputs due to crowding

1. When communication costs high → split costly → low demand for labour from spatially disintegrated firms → firm will pay low wages

2. When communication costs low → separation efficient → cities specialized by function → each function benefit from specific agglomeration effects → headquarters will pay higher wages