HOW TO MEASURE ECONOMIES OF
AGGLOMERATION
Measures of spatial concentration
Properties of an ideal index 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
Measures of concentration
•
•
•
•
•
E = employment
s = ratio
i = sector i= 1,……., N
j = region j= 1,……., M
Eij employment in sector i in region j
• E j   Eij
total employment of region j
i
• Ei   Eij total employment of sector i
j
• E   Eij total employment in the country
i
j
Coefficient of specialization
s 
e
ij
Eij
si 
Ej
Ei
E
Coefficient of specialization of region j in sector i 
sije
si
Localization coefficient (or Hoover-Balassa)
s 
c
ij
Eij
Ei
sj 
Ej
E
Coefficient of localization of sector i in region j 
sijc
sj
Herfindhal index
 1
1, n 
n
H   ( sije )2
e
j
i 1
m
H   ( sijc ) 2
c
i
j 1
 1
1, m 
Index of Isard
IDEAj 
1
sije  si

2 i
0,1
IDCAi 
1
c
s

ij  s j
2 j
0,1
The Gini Index
The most popular index for measuring inequality
Here we use it to evaluate the spatial concentration of a given sector in terms of
employment
n
S j n    s j
Cumulative percentage of s j
j 1
m
Gi  1   s j  Sijc n1  Sijc n  


n 1
Region
sijc
sj
sijc s j
Sijc
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
Sj
ODCBA
ODE
ODE  1 ·1·1  0.5
2
G
ODCBA  ODE  (OAI  ABGI  BCFG  CDEF )
OAI  1 2  0.2  0.1
ABGI  1 2  (0.1+0.3)  (0.45-0.2)
BCFG  1 2  (0.3+0.6)  (0.7-0.45)
CDEF  1 2  (0.6+1)  (1-0.7)
ODCBA  0.5  0.4125  0.0875
G
0.0875
 0.175
0.5
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)
Specialization
n
Eij
i 1
Ej
SI jk  
Eij
Localization
Lij 
EiUS
Ej
EUS

Eik
Ek
Specialization. Average of bilateral indexes
Localization. Average of Hoover-Balassa
First: trend due to half of sectors
that increase weight
Second: 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
Locationit  0  1PlantSizeit  2 RawMatIntensityit  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 of
the twentieth century, firms adopted large-scale production methods
that were intensive in relatively immobile resources and energy
sources.
- 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 z1 ,..., zl ,..., zN the percentage
of employment across the plants of the sector
The correlation between the location choices of two plants l and k belonging
to the same sector is an index:
  corr  ulj , ukj 
where
ulj  1 If plant l in sector i is located in region j and
ulj  0 otherwise
If   0 , location choices are independent, which corresponds to a random
distribution 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 a
a 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
P  ulj  1  s j
i
GEG
i
ˆEG
i
EG
G
 Hi


2
1   s j 
j


1  H i 

  s  sj
c
ij

2
Ellison-Glaeser index
Spatial Gini index
j
 l production establishment

H i   z Industrial H-H index 

z
establishment's
employment
share
of
industry
l


2
il
i
ˆEG
 0 Random concentration (spatial concentration is a result of industrial concentration)
ˆ iEG  0 Concentration higher than random concentration
Plant
Ranking Spatial
Herfindahl
Gini
Leather & Leather Products
0.0253
5
0.074
Textile Mill Products
0.0018
19
0.0171
Instruments & Related Products
0.0083
9
0.0219
Rubber & Miscellaneous Plastics Products
0.0041
12
0.0163
Lumber & Wood Products
Fabricated Metal Products
Printing & Publishing
Furniture & Fixtures
Primary Metal Industries
Paper & Allied Products
Industrial Machinery & Equipment
Food & Kindred Products
Chemical & Allied Products
Apparel & Other Textile Products
Stone, Clay, & Glass Products
Electrical Material & Equipment
Other Transportation Material
Electronic Equipment
Motor Vehicles
Computer & Office Equipment
0.0023
0.0008
0.0025
0.0028
0.0174
0.0066
0.0025
0.0039
0.005
0.0027
0.0129
0.0119
0.0545
0.0645
0.1016
0.2391
18
20
16
14
6
10
17
13
11
15
7
8
4
3
2
1
0.0143
0.0123
0.0129
0.0129
0.0256
0.0147
0.0085
0.0088
0.0086
0.0061
0.0142
0.0051
0.0371
0.0108
0.0261
0.0459
Ranking Ellison &
Glaeser
1
0.0500
7
0.0153
6
0.0137
8
0.0122
10
14
12
13
5
9
18
16
17
19
11
20
3
15
4
2
0.0120
0.0115
0.0104
0.0101
0.0083
0.0081
0.0060
0.0049
0.0036
0.0034
0.0013
-0.0069
-0.0184
-0.0574
-0.0840
-0.2539
Ranking
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
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
County
Zipcode
•
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
y j  g  Aj  f  x j 
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)
•
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
denempc 
Employmentc
Areac
- Measures of specialization of city in sector espcs 
employmentcs
coef espcs 
employmentcs
employmentc
or
employmentc
employmentcountry ,s
employmentcountry
- Measures of industrial diversity of the city
 employmentcs 
Hc  

s  employmentc 
2
•
Wages
Assumption:
In competitive markets
w  VMPL
Even without perfect competition, in more productive locations, wages will be higher
Economies of agglomeration  Higher productivity  Higher wage
wij  f  individualcharacteristics, agglomeration variables 
Microdata on wages increasingly available
•
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
NoFirms  f  Agglomeration variables, Other controls  competition, input costs,... 
•
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
ln E1  ln E0  f (Agglomeration variables0 , Other control variables0 )
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 l j
kj
And other factors

Production function given by: y j  Aj  s j l j  k 1j
  is the proportion of labor in production
 A j is a Hicks-neutral factor augmenting technology level
 s j is the efficiency level of workers
Profit of the firm:
 j   p jb y jb  wj l j  rj k j  p j y j  w jl j  rj k j
b
y jb is the quantity exported to region b, p jb is the mill price set in region b
net of the marginal cost of intermediate inputs,
p j   p jb
b
y jb
yj
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
 p j y j  is the value added of the firm (Value of production minus cost of
intermediates)
wj
rj
Applying FOC and rearranging terms:
1 
 kj 
w j   p j Aj s j  
l 
 j

 kj 
rj  (1   ) p j Aj s j  
l 
 j


By plugging the second expression into the first, we obtain:
1 
w j   (1   )

 p j Aj
s j  1 
 r
 j
1/ 



By aggregating:
1 
wrs 
 (1   )
nrs

1/ 
 p j Aj 
s j  1  

 r

j( rs )
 j 
nrs is the number of firms in region r and sector s
In which region is the marginal productivity of labor the highest?
1 
w j   (1   )

p A
s j  1j  j
 r
 j
1/ 



The equation shows that wages are directly proportional to workers’ efficiency, s j
This has to do with workers’ endowments but not with space
Still we have
p j , rj , Aj
through which agglomeration effects show up
 A higher p j , 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.
 rj 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
 Technological externalities are taken into account through A j
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:
pj yj
lj
 (1   )
1   
1/ 
p A 
sj 

 r


1 
j
j
1 
j
pj yj
l j k 1j  
 p j A j s j
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
ln wrs     lndenr   rs
where
denr 
empr
arear
Estimating the above equation is equivalent to estimate:
1
ln
nrs
•
 p j Aj
s j  1 

 r
j( rs )
 j



1

    lndenr   rs
Implicit assumption:
Density affects wage level through: the local level of technology, A ;j the output price, ; p j
the prices of other inputs, rj; the local efficiency of labor, s j
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
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
spers 
emprs
specialization index captures intraindustry externalities
empr
For interindustry externalities, an “industrial diversity” variables is included
(Herfindhal index)
  emp  2 
rs  
divr   

 s  empr  
1
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  rs
Problem: Supply of LPG greater in areas characterized by concentrated
activity (public policy decisions)
Consequence: overestimation of density effect
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 increasing
Negative shocks may expel workers from the affected regions
Shocks can have effects on the attraction of regions

Impact on activity

Impact on employment density

corr (ln dens ,  rs )  0
Inverse causality: Shocks → w → attraction/expulsion of workers →
Increase/Decrease of density
Low mobility of factors weaker bias
However, still endogeneity bias through creation/destruction of jobs
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:
ln denr   ln denr ,t 150  r
This provides us with a prediction of density:
ˆ  ˆ ln denr ,t 150 where ˆ is the OLS estimator for
ln den

2. The density in the initial regression ln wrs     ln denr   rs
is replaced by its predicted value ( denr is instrumented) which uncorrelated
with the residuals since the instrument is by construction exogenous:
ˆ r ,  rs   corr  ˆ ln denr ,t 150 ,  rs 
corr  ln den
 corr  ln denr ,t 150 ,  rs 
0
The OLS estimate of the equation no longer suffers from endogeneity bias
ln wrs     ln deˆnr   rs
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