HOW TO MEASURE ECONOMIES OF AGGLOMERATION

Measures of spatial 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

i

Es

E

Coefficient of specialization

eij

i

s

sCoefficient of specialization of region j in sector i

ijcij

i

Es

E j

j

Es

E

Localization coefficient (or Hoover-Balassa)

cij

j

s

sCoefficient of localization of sector i in region j

Herfindhal index

2

1

( )n

e ej ij

i

H s

11,

n

1

2e

j ij ii

IDEA s s

2

1

( )m

c ci ij

j

H s

11,

m

1

2c

i ij jj

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

ODCBAG

ODE

ODE

( )ODCBA ODE OAI ABGI BCFG CDEF

1 2 0.2 0.1OAI

1 2 (0.1+0.3) (0.45-0.2)ABGI

1 2 (0.3+0.6) (0.7-0.45)BCFG

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

0.5 0.4125 0.0875ODCBA

0.08750.175

0.5G

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 specialization and concentration of manufacturing in the long term

- Externalities - H-O- Internal increasing returns

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 ESI

E E

ij

iUSij

j

US

EE

LE

E

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.

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

1

ˆ Ellison-Glaeser index1

Spatial Gini index

production establishment Industrial H-H index

establishment's employment share of industry

iEG

i

jji

EGi

i cEG ij j

j

i ill

GH

s

H

G s s

lH z

z

ˆ 0 Random concentration (spatial concentration is a result of industrial concentration)

ˆ 0 Concentration higher than random concentration

iEG

iEG

Plant Herfindahl

Ranking Spatial Gini

Ranking Ellison & Glaeser

Ranking

Leather & Leather Products 0.0253 5 0.074 1 0.0500 1

Textile Mill Products 0.0018 19 0.0171 7 0.0153 2

Instruments & Related Products 0.0083 9 0.0219 6 0.0137 3

Rubber & Miscellaneous Plastics Products 0.0041 12 0.0163 8 0.0122 4

Lumber & Wood Products 0.0023 18 0.0143 10 0.0120 5

Fabricated Metal Products 0.0008 20 0.0123 14 0.0115 6

Printing & Publishing 0.0025 16 0.0129 12 0.0104 7

Furniture & Fixtures 0.0028 14 0.0129 13 0.0101 8

Primary Metal Industries 0.0174 6 0.0256 5 0.0083 9

Paper & Allied Products 0.0066 10 0.0147 9 0.0081 10

Industrial Machinery & Equipment 0.0025 17 0.0085 18 0.0060 11

Food & Kindred Products 0.0039 13 0.0088 16 0.0049 12

Chemical & Allied Products 0.005 11 0.0086 17 0.0036 13

Apparel & Other Textile Products 0.0027 15 0.0061 19 0.0034 14

Stone, Clay, & Glass Products 0.0129 7 0.0142 11 0.0013 15

Electrical Material & Equipment 0.0119 8 0.0051 20 -0.0069 16

Other Transportation Material 0.0545 4 0.0371 3 -0.0184 17

Electronic Equipment 0.0645 3 0.0108 15 -0.0574 18

Motor Vehicles 0.1016 2 0.0261 4 -0.0840 19

Computer & Office Equipment 0.2391 1 0.0459 2 -0.2539 20

Rosenthal and Strange (2001) “Determinants of agglomeration”

High level of concentration indicative of agglomeration economies but also other explanations.

R&S objective: to evaluate the degree to which agglomerative externalities explain inter-industry differences in spatial concentration.They regress Index of Ellison-Glaeser on proxies of sources of agglomeration Fourth quarter 2000

Variables

Controls for natural advantage and transportation costs

Energy per $ shipment

Natural resources per $ shipment

Water per $ shipment

To the extent that industries concentrate because of a desire to locate close to the sources of their energy, natural resources, and water realted inputs, expectation of positive coefficients of these variables

Inventory per $ of shipment (Transportation cost).

1.Value of the end-of-year inventories divided by the value of shipments 2.Data on actual product shipping costs by industry not suitable: industries with high transport rate locate so as to minimize distances to their markets and the related shipping costs.3.Industries that produce highly perishable products face high product shipping costs per unit of distance.4.With multiple markets, less agglomeration. Conversely for non perishable

Controls for agglomerative externalities

Sharing Manufactured inputs per $ of shipment Nonmanufactured inputs per $ of shipment

• Manufactured:

Larger economies of scale Greater industry specificity

• Expectation: non-manufactured less impact on agglomeration  Learning

Innovations per $ of shipment Innovations defined as the number of new products advertised in trade magazines in 1982, the only year for which such data are available

Matching

• If matching is possible, an industry benefits by agglomerating because it is better able to hire workers wiyh industry-specific skills.

• It is difficult to identify industry characteristics that are related to the specialization of the industry’s labour force

Three proxies:

Net productivity (Value of shipments less the value of purchased inputs divided by the number of workers in the industry)

Management workers/ (Management workers+ Production workers)

% of workers with doctorates, Master’s degree, and Bachelor’s degree

Strategy:

• They estimate equations for concentration measures at three different levels of spatial detail:

State CountyZipcode

• Does different sources operate at different spatial scales?

Results

Natural advantage and transportation costs

Natural advantage (except energy). Significant at state level

Inventories. Significant at state level (Industries with output that is costly to transport are more likely to locate close to their markets → less agglomeration)

Sharing

Manufactured inputs. Significant at state level

Nonmanufactured inputs. Negative coefficient and significant at state level

A reliance on manufactured inputs contributes to agglomeration

A reliance on service inputs does not (constant returns to scale and not industry specific → available everywhere)

Matching

Net productivity. Significant at the three levels

Managerial share of workers. Significant at county and zipcode level

Master’s degree. Significant at the three levels

Learning

Innovations. Significant at zipcode level

Reliance on manufactured and naturally occurring inputs and the production of perishable products serve to increase the importance of shipping costs in firm location

That, in turn, positively affects state-level agglomeration but has little effect on agglomeration at lower levels

Knowledge spillovers positively affect agglomeration at highly localized levels

Reliance on skilled labor affects agglomeration at all levels

MEASURING ECONOMIES OF AGGLOMERATION

• Agglomeration economies imply that firms located in an agglomeration are able to produce more output with the same inputs

The most natural and direct way to quantify agglomeration economies is to estimate the elasticity of some measure of average productivity with respect to some measure of local scale, such as employment density or total population

MODELING APPROACHES

• Production Function

The most natural and direct way to measure economies of agglomeration

Fundamental challenge is to find data on all inputs

The easiest to find: - Employment/Hours of work

The rest not so easy: - Physical capital - Land - Materials (purchased by the firm not made by the firm)

j j jy g A f x

• Measures of A (s sector, c city)

- Size of employment (nº de firms) from firm’s industry in the city (economies of localization) - Size of employment or population of the city (economies of urbanization)

- Employment density

- Measures of specialization of city in sector or

- Measures of industrial diversity of the city

cc

c

Employmentdenemp

Area

cscs

c

employmentesp

employment

,

cs

ccs

country s

country

employmentemployment

coef espemployment

employment

2

csc

s c

employmentH

employment

• Wages

Assumption: In competitive markets

Even without perfect competition, in more productive locations, wages will be higher

Economies of agglomeration Higher productivity Higher wage

Microdata on wages increasingly available

w VMPL

individualcharacteristics, agglomeration variablesijw f

• Births of new establishments

Assumption: Entrepreneurs seek out profit-maximizing locations and are disproportionately drawn

to the most productive regions Economies of agglomeration Higher productivity Higher profit Location

decision

No need of data of purchased inputs New establishments are largely unconstrained by previous decisions Decisions are made taken as exogenous the existing economic environment

Agglomeration variables, Other controls competition, input costs,...NoFirms f

• Employment Growth

Assumption: Agglomeration economies enhance productivity and productive regions

grow more rapidly as a result

Economies of agglomeration Higher productivity Shift labor demand Employment growth

Data on employment easily available

1 0 0 0ln ln (Agglomeration variables , Other control variables )E E f

DETERMINANTS OF LOCAL PRODUCTIVITY

We will see how can be derived an estimable equation relating productivity/wage and agglomeration economies, taking as a departure point a production function

We assume a firm j Located in r Operating in sector s Using labor in quantity And other factors Production function given by: is the proportion of labor in production is a Hicks-neutral factor augmenting technology level is the efficiency level of workers

jl

jk

1j j j j jy A s l k

jA

js

Profit of the firm:

is the quantity exported to region b, is the mill price set in region b net of the marginal cost of intermediate inputs,

is the average unit value, net of the cost of the intermediate inputs is the wage rate is the cost of inputs other than labor and intermediate inputs is the value added of the firm (Value of production minus cost of

intermediates)

j jb jb j j j j j j j j j jb

p y w l r k p y w l r k jby jbp

jbj jb

b j

yp p

y

jw

jr

j jp y

Applying FOC and rearranging terms:

1

jj j j j

j

kw p A s

l

(1 ) jj j j j

j

kr p A s

l

1/1

1(1 ) j j

j jj

p Aw s

r

11/

1( )

(1 ) j jrs j rs

j rsrs j

p Aw s n

n r

By plugging the second expression into the first, we obtain:

By aggregating:

is the number of firms in region r and sector s

In which region is the marginal productivity of labor the highest?

The equation shows that wages are directly proportional to workers’ efficiency,

This has to do with workers’ endowments but not with space

Still we have through which agglomeration effects show up

A higher , because of high demand, weak competition or cheap intermediates, positively affects wages and worker attraction contributing to a higher degree of agglomeration in the region.

captures the effects transmitted through other factor prices. When production factors have a low supply elasticity (e.g., land), prices will be higher

in agglomerated areas, which pushes down the wage rate and are affected by pecuniary externalities that work through market mechanisms

1/1

1(1 ) j j

j jj

p Aw s

r

js

, ,j j jp r A

jp

jr

Technological externalities are taken into account through Regions with easy circulation of information and/or high concentration of skilled

workers are likely to benefit from more productive technologies, then higher wages.

Conversely, transport congestion or pollution worsen productivity and wages

Alternatively, if data related to value-added and capital stocks are available:

jA

1/1

1

1(1 )j j j j

jj j

p y p As

l r

1

j jj j j

j j

p yp A s

l k

ECONOMETRIC ISSUES

We regress the total factor productivity, average labor productivity or nominal wage on the employment or population density. We can use logs to interpret the coefficient directly as an elasticity

where

Estimating the above equation is equivalent to estimate:

• Implicit assumption:

Density affects wage level through: the local level of technology, ; the output price, ; the prices of other inputs, ; the local efficiency of labor,

Not able to determine through which variables. Only the net effect of density is identified

But this still relevant for policies designed to concentrate or disperse activities

ln lnrs r rsw den rr

r

empden

area

1

1( )

1ln lnj j

j r rsj rsrs j

p As den

n r

jA jpjr js

Omitted variables

1. Skills

Differences of skill across space partly explain productivity differentials

Not controlling for average regional skill levels labor skills are randomly distributed across regions and captured by the error term

If skill controls are not introduced:If denser areas are more skilled, the effect of density will be overestimated

2. Intra and Inter-sectorial externalities

Wage varies by region and sector but density only varies by region Industrial mix should be controlled

Industrial mix is important where: • output is sold to a small number of industries • inputs used are industry specific

it affects the level of productivity through price effects

specialization index captures intraindustry externalities

For interindustry externalities, an “industrial diversity” variables is included (Herfindhal index)

r

rsrs emp

empspe

12

s r

rsr emp

empdiv

3. Natural amenities and local public goods

Amenities:• Naturals: favorable climate, coast-line location, presence of lakes and mountains, natural

endowments in raw materials• Man-made: the result of public policy like leisure facilities (theaters, swimming pools,…) or

public services (schools, hospitals,…)

Local Public Goods → benefits reaped by local consumers

LPG can be used by firms: Transport infrastructures, research laboratories, job training centers LPG can affect productivity of production factors If randomly located → captured by Problem: Supply of LPG greater in areas characterized by concentrated activity (public

policy decisions) Consequence: overestimation of density effect

rs

But amenities may have additional effects On the supply side: If a region has amenities that attract population → Upward pressure on

demand for housing → Pushing up rents On the demand side:Higher land rents → Higher cost for firms → Substitute other production

factors, labor, for land → Marginal productivity of labor decreases → Drop in wages

If natural amenities are more abundant in heavily populated regions (e.g., leisure facilities) the effect of density is underestimated

4. Effects of interaction with neighboring regions

Some form of density market potential

5. ¿Using fixed effects?

If available a panel of industries and regions, it is possible to use fixed effects to control for omitted variables

We need to make the assumption that during the panel period, the omitted we want to control for are constant. For example, amenity and public good endowments

Endogeneity bias

OLS estimates are biased when some explanatory variables are correlated with the residuals of the regression. These variables are said to be endogenous

Assume that a given region experiences a shock observed by economic agents but overlooked by the researcher:

Positive shock → some correct decisions made by the regional government that increases productivity

Negative shock → an increase of oil price negatively affects regions with intensive use of oil

If shocks are localized and affect the location of agents:Positive shocks may attract workers to the affected region where wages are increasingNegative shocks may expel workers from the affected regions

Shocks can have effects on the attraction of regions

Impact on activity

Impact on employment density

Inverse causality: Shocks → → attraction/expulsion of workers → Increase/Decrease of density

Low mobility of factors weaker bias However, still endogeneity bias through creation/destruction of jobs

(ln , ) 0s rscorr den

w

Most common approach to address the problem:

Instrumental variables technique finding variables (instruments) correlated with the endogenous variable but not with the residual

1. The first step is regressing the variable we consider endogenous on the chosen instrument.

Ciccone & Hall (1996) are the first to take into account the problem of endogeneity in this context. They use as an instrument past density.

Instrumental regression:

This provides us with a prediction of density: where is the OLS estimator for

, 150ln lnr r t rden den

, 150ˆˆln ln r tden den ̂

2. The density in the initial regression is replaced by its predicted value ( is instrumented) which uncorrelated with the

residuals since the instrument is by construction exogenous:

The OLS estimate of the equation no longer suffers from endogeneity bias

Crucial point: assumption of exogeneity of the instrument

Assumption: there is persistence in agglomeration but there is no correlation between past employment density and present productivity shocks

Nevertheless a long lag is not a sufficient condition:The source of a shock may be linked to unobserved factors that persist over time

ln lnrs r rsw den

rden

, 150

, 150

ˆˆln , ln ,

ln ,

0

r rs r t rs

r t rs

corr den corr den

corr den

rsrrs nedw ˆlnln