Lecture 2: Urban Agglomeration EconomiesWWS 538

Esteban Rossi-Hansberg

Princeton University

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 1 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 2 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 3 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 4 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 5 / 19

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 ) Lecture 2: Urban Agglomeration Economies 6 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 7 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 8 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 9 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 10 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 11 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 12 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 13 / 19

Software

62

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 14 / 19

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

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 15 / 19

Population Density

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 16 / 19

Real Income per Capita

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 17 / 19

Productivity

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 18 / 19

Amenities

ERH (Princeton University ) Lecture 2: Urban Agglomeration Economies 19 / 19