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

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

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 is

likely to stay there long: so great are the advantages which

people following the same skilled trade get from near

neighbourhood to one another. The mysteries of the trade

become no mysteries; but are as it were in the air, and

children learn many of them unconsciously. Good work is rightly

appreciated, inventions and improvements in machinery, in

processes and the general organization of the business have their

merits promptly discussed: if one man starts a new idea, it is

taken 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.

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.

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·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

The Geography of Innovation and Production

Innovative activity tends to cluster spatially

1. Geographic concentration of innovation varies by industry2. Does not coincide with geographic concentration of production

Traditional arguments for concentration of production Dependency on natural resources Low transportation costs Large economies of scales

Clustering of innovation when new knowledge is particularly important Industry expenditure on R&D relative to sales Share of skilled workers in industry employment University research relevant to the industry

Indirect evidence of knowledge spillovers

Externalities of human capital

• The productivity of individual workers is enhanced by an environment of high human capital

• Labor and education policy Social returns to skill > private returns to skill Education as a public good Rationale for vast government intervention

• Endogenous growth theory Lucas (1988) allows a country’s average human capital to increase TFP

Standard approach to the analysis of human capital externalities

i a iy A B h

An economy with workers i or j, living in cities a.

The social output of worker i with human capital hi and living in city a is given by:

A is a technological parameter independent of location and Ba is a city specific parameter.

The earnings of this worker are:

i i aw Ah D

a i aB h D Reciprocal externality

The cost of human hi:

1i i iC c h

imax w iC

11

ii

Ah

c

max i iy C

11

ai

i

A Bh

c

• Lucas (1988): “Most of what we know we learn form other people. We pay tuition to only a few of these teachers, either directly or indirectly by accepting lower pay so we hang around them, but most of it we get for free, and often in ways that are mutual- without distiction between student and teacher”

Assume that worker i’s human capital directly benefits N other workers in the city by an amount

At the same time, worker i also benefits from the human capital investment made by all other workers in the interaction group.

Summing across all workers j part of the interaction group of worker i:

a i a i i a i i iB bN y A B h Ah B h Ah bh N

a j a j aj j

D bh bNh h Nh

Where ah is the average human capital in city a and N is the size of the

interaction group. So we can write now:

i i a i aw Ah D Ah bNh

ibh

i i a i aw Ah D Ah bNh

This equation can be estimated by means of regression analysis

21 2log exp expij ij ij ij j ijw s s

i individual j city

Rauch (1993) is the first

0

There exist human capital externalities is

Rauch finds between 0.03-0.05

HOW TO MEASURE ECONOMIES OF AGGLOMERATION

Production function: Q = f(K,L)

Q = units of output

L = units of labour

K = units of capital

Suppose a production function has the form

(Cobb-Douglas)

If , then there is constant returns to scale.

If , then there are economies of scale

Q K L

1

1

Example: Suppose K and L both double. Then we have:

So output increases by

This means output more than doubles if

.

The elasticity of output with respect to L equals and the elasticity of

output with respect to K equals .

(Elasticity is the percentage change in output that occurs when labor or capital increases by one percent.)

2 ( )Q K L

2

1

How to incorporate agglomeration economies into the production

function? The idea of agglomeration economies is that economies of scale

Also depend on the size of the city. Change the production function to:

where N is the population of the city or the number of firms in the city

The elasticity of output with respect to the population of the city N is

If there are no agglomeration economies, then =0. Then if the population

of the city doubles (substitute 2N for N), then output will be multiplied by

, i.e., it won’t change

If there are agglomeration economics, then . This means that firms

are more efficient if they are located in larger cities. (Could alternately

define N as the number of firms in the city.)

( )Q N K L

02 1

0

Example: suppose . Then if the population of the city doubles,

output will be multiplied by , i.e., output rises by 7%.

How to test this?

Ideally, this would be tested for particular industries. Get data on number

of workers who work in the (say) shoe industry in each city (L) and the

amount of capital in the shoe industry in each city (K) and the number of

shoe manufacturing firms in each city (N), and the number of pairs of shoes

produced in each city.

0.10 0.102 1.0718

This gives us a dataset of values of Q, K, L, and N for each city in the U.S.

Then run a regression that explains Q using K, L, and N. It gives us

estimates of . If , then there are agglomeration economies in

the shoe industry. (Note: regression analysis next time.)

This type of function has been estimated:

Results:

for the electrical machinery industry,

0.02 for the pulp and paper industry,

0.11 for the petroleum industry.

0.27 in the office industry.

These effects are small, but they can be important in giving large cities an

advantage over small ones.

, , 0

ln ln ln lnQ N K L

0.05

Wages

In competitive markets labour is paid the value of its marginal product

Larger employment size/density Higher productivity Higher wage

ln ln / varw employment density size control iables

Urban wage premium

But not the only possible reason for higher wages in larger cities

1. Sorting of the skilled into cities?2. Human capital accumulation?

So

Two basic questions:Is it that most skilled sort into cities or that cities improve productivity?Is the effect important when people get to the city or do wages grow over time faster?

Sorting

• Most skilled might sort into cities because:

– Information flows are relatively more valuable to them

– Consumption amenities might be more attractive for skilled people

• If wages are higher cities, why workers do not flock to higher wage cities?

• If wages are higher cities, why firms do not flee the higher wage cities?

Labour supply

In order to have a spatial equilibrium real wages per unit of skill equalize:

needs to be constant across cities i

units of skill wage in city i price index in city i

Implies that

So if , there are no ability differences across cities

k i

iP

k i iP

log ii j i j

j

PW W

P

log 0ii j i j

j

PW W

P

Labour demand

• In order for firms to demand workers in a city and pay higher wages it most be that they

Obtain higher productivityCharge higher prices because transport costs are lower

• Suppose firms maximize:

is labor in unit of efficiency and includes efficiency and pricesThen, firm maximization and zero profits imply

• Implies that

For firms to stay in high wage areas, either workers in those areas have higher ability levels or productivity must be higher in those areas

The goal is to obtain an estimate of

1i iAK L L RK

L iA

1i icR L RK

1log

1i

i j i jj

AW W

A

i

j

AA

Robust evidence for wage premium France 5%, US 4.1%, Spain 4.8%

But when controlling for sorting (individual fixed effects), premium reduction France 35% , Spain 46% (no clear evidence in US)

Timing effects

Most standard theories imply that effects happen at impact So wages should jump up when people move to cities and should jump down when they move out

Alternatively, cities might act through human capital accumulation or labor-market matching

In this case wages should grow over time and should not jump down when worker leave

Spain: Experience accumulated in bigger cities more valuable than experience accumulated elsewhere

First year of experience in Madrid or Barcelona raises earnings by 2.7% relative to having worked in a city below top five

Most of the earnings premium in bigger cities is not instantaneous but accumulates over time and highly portable

Sources of Agglomeration

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 explainInterindustry differences in spatial concentration.

•They regress a measure of industry concentration on proxies of sources of agglomeration

• Fourth quarter 2000

Variables used

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 shipments2. 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 realted 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: nonmanufactured 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, Masrter’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 ocurring inputs and the production of perishable products serve to increase teh 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 labour affects agglomeration at all levels