Lecture 7: Industrial Concentration and Systems of Citieserossi/Urban/Lecture_7_538.pdf · Lecture 7: Industrial Concentration and Systems of Cities WWS 582a Esteban Rossi-Hansberg

Lecture 7: Industrial Concentration and Systems ofCities

WWS 582a

Esteban Rossi-Hansberg

Princeton University

ERH (Princeton University ) Lecture 7: Ind. Conc. and Systems of Cities 1 / 40

Duranton and Overman (2005)

Need a way to measure industrial concentration

What seems like industrial concentration might be misleading due to thesmall number of plants

I The law of large numbers does not apply

Ellison and Glaeser (1997) dartboard approachI E.g. 75% of the employees in the U.S. vacuum cleaner industry work in one offour main plants

I Even if these plants locate separately, four locations must account for at least75% of the employment in this industry without it being localized in anymeaningful way


Some Examples1082 REVIEW OF ECONOMIC STUDIES

(a) Basic Pharmaceuticals(SIC2441)

(b) Pharmaceutical Preparations(SIC2442)

(c) Other Agricultural and ForestryMachinery (SIC2932)

(d) Machinery for Textile, Apparel andLeather Production (SIC2954)

FIGURE 1

Maps of four illustrative industries

at Princeton University on A

pril 4, 2012http://restud.oxfordjournals.org/

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Characteristics of a Measure of Localization

Any test of localization should rely on a measure which:1 is comparable across industries;2 controls for the overall agglomeration of manufacturing;3 controls for industrial concentration;4 is unbiased with respect to scale and aggregation

Their measure considers the distribution of distances between pairs ofestablishments in an industry and compares it with that of hypotheticalindustries with the same number of establishments which are randomlydistributed conditional on the distribution of aggregate manufacturing


The Measure of Localization

Data selection: Sometimes cutting out the lower tail might be useful becauseestablishments do something else

Let dij denote the distance between establishments i and j then theK−density at distance d is given by

K (d) =1

n (n− 1) hn−1∑i=1

n

∑j=1+1

f(d − dijh

)where f is the Gaussian kernel, n is the number of establishments, and h isthe bandwidth.

Need to use a Kernel comes form the error in measuring "effective distance"

Note that the number and size of plants is taken as given


The Examples1084 REVIEW OF ECONOMIC STUDIES





0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

FIGURE 2

K -density, local confidence intervals and global confidence bands for four illustrative industries

the entire industry population. If, instead of a census, we had a random sample of firms from eachindustrywe would need to worry about the statistical variation due to the estimation of the actualK -density. Applications of the techniques developed below to samples of firms from particularindustries could allow for this statistical variation to be taken into account but the exhaustivenature of our data means that we are able to ignore it in what follows (seeEfron and Tibshirani,1993, andQuah,1997, for further discussion of these issues as well asDavison and Hinkley,1997, for a discussion more focused on point patterns).

Thesecond difference stems from the fact that the spatial nature of our data implies strongdependence between the bilateral distances that are used to calculate the density. This strongdependence arises because the observations of interest are actually the points that generatethese bilateral distances. Even if the underlying points are independently located, the bilateraldistances between these points will not be independent.6 This has implications for the samplingtheoryof our estimator,K A(d). In situations where the observations are independent (or only

6. See below for more on this issue.



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Counterfactuals

Still need to control for the overall tendency of manufacturing to agglomerate

Draw locations for plants in feasible "sites" and calculate the counterfactualdensity fixing the number of plants

I Sampling without replacement

Run many simulations and take the top 5% and lowest 5% in the generatedsample

The result is a confidence interval for what would happen if the industry wasrandomly located

When for industry A, KA(d) > KA(d), this industry is said to exhibitlocalization at distance d (at a 5% confidence level)

Symmetrically, when KA(d) < KA(d), this industry is said to exhibitdispersion at distance d (at a 5% confidence level)


The Index

Define an index of localization as

γA (d) ≡ max(KA(d)−KA(d), 0

)To reject the hypothesis of randomness at distance d because of localization(dispersion), we only need γA (d) > 0

Similarly the dispersion index is calculated as

ψA (d) ≡ max(KA(d)− KA(d), 0

)Similarly global measures are calculated when we use a bound determined bythe top 5% or realizations at any given distance


The Examples1084 REVIEW OF ECONOMIC STUDIES





0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

0·005

0·004

0·003

0·002

0·001

0·0000 20 40 60 80 100 120 140 160 180

Distance (km)

FIGURE 2

K -density, local confidence intervals and global confidence bands for four illustrative industries

the entire industry population. If, instead of a census, we had a random sample of firms from eachindustrywe would need to worry about the statistical variation due to the estimation of the actualK -density. Applications of the techniques developed below to samples of firms from particularindustries could allow for this statistical variation to be taken into account but the exhaustivenature of our data means that we are able to ignore it in what follows (seeEfron and Tibshirani,1993, andQuah,1997, for further discussion of these issues as well asDavison and Hinkley,1997, for a discussion more focused on point patterns).

Thesecond difference stems from the fact that the spatial nature of our data implies strongdependence between the bilateral distances that are used to calculate the density. This strongdependence arises because the observations of interest are actually the points that generatethese bilateral distances. Even if the underlying points are independently located, the bilateraldistances between these points will not be independent.6 This has implications for the samplingtheoryof our estimator,K A(d). In situations where the observations are independent (or only

6. See below for more on this issue.



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Findings Across Industries

1090 REVIEW OF ECONOMIC STUDIES

TABLE 1

Localizationat three thresholds for four-digit industries

Percentage of four-digit industries localized at:

5 km 5 km only 5 and 30 km only 5 and 150 km only 5, 30 and 150 km39·3 6·4 22·6 0·9 9·4

30 km 30 km only 30 and 150 km only38·9 6·0 0·9

150 km 150 km only17·1 6·0

(a) Global localization

100

90

80

70

60

50

40

30

20

10

00 20 40 60 80 100 120 140 160 180

Distance (km)

(b) Global dispersion

100

90

80

70

60

50

40

30

20

10

00 20 40 60 80 100 120 140 160 180

Distance (km)

(c) Local localization

100

90

80

70

60

50

40

30

20

10

00 20 40 60 80 100 120 140 160 180

Distance (km)

(d) Local dispersion

100

90

80

70

60

50

40

30

20

10

00 20 40 60 80 100 120 140 160 180

Distance (km)

FIGURE 3

Number of four-digit industries with local/global localization and dispersion

across distances, but not across the two figures.13 It is immediately apparent that the extent oflocalizationis much greater at small distances than large distances. As before, dispersion doesnot show any marked pattern. The important conclusion we draw here is that localization tendsto take place mostly at fairly small scales.

13. This is because for an industry that exhibits localization the density is unbounded from above whereas thedensityof an industry that exhibits dispersion is bounded from below by zero.



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Taking Intensity into AccountDURANTON & OVERMAN TESTING FOR LOCALIZATION 1091

(a) Global localization

0·240·220·200·180·160·140·120·100·080·060·040·020·00

0 20 40 60 80 100 120 140 160 180Distance (km)

(b) Global dispersion

0·240·220·200·180·160·140·120·100·080·060·040·020·00

0 20 40 60 80 100 120 140 160 180Distance (km)

FIGURE 4

Index of global localization and dispersion by distance

0·50

0·45

0·40

0·35

0·30

0·25

0·20

0·15

0·10

0·05

0·000 20 40 60 80 100120140160180200220240

FIGURE 5

Distribution of global localization and dispersion by four-digit industries

Differences between industries

We now turn to the examination of differences between industries. We start by constructinga measure of the extent to which different industries deviate from randomness. Proceedingas before, for each industryA we can define the following cross-distance indices:0A ≡∑180

d=00A(d), and9A ≡∑180

d=09A(d). Respectively, these measures are the sum for eachindustry of the index of global localization and dispersion across all levels of distance. Toillustrate the variations in industry outcomes, we rank industries by decreasing order of theseindices and plot them inFigure 5. The upper line is the measure of localization, the lower that ofdispersion.As is immediately clear, there are a few industries that show very high localization ordispersion, but the majority of industries do not see such extreme outcomes. This highly skeweddistribution of localization confirms previous findings (Ellison and Glaeser(1997),Maurel andSedillot (1999),Devereuxetal. (2004)).

To give some idea of the reality underlyingFigure 5,Table 2lists the 10 most localizedindustriesand the 10 most dispersed. Interestingly, more than a century afterMarshall(1890),Cutlery (SIC2861) is still amongst the most localized industries. Six textile or textile-related



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Particular Industries

1092 REVIEW OF ECONOMIC STUDIES

TABLE 2

Mostlocalized and most dispersed four-digit industries

SIC92 Industry 0 or9

Most localized

2214 Publishing of sound recordings 0·4701711 Preparation and spinning of cotton-type fibres 0·4112231 Reproduction of sound recordings 0·4031760 Manufacture of knitted and crocheted fabrics 0·3211713 Preparation and spinning of worsted-type fibres 0·3192861 Manufacture of cutlery 0·3141771 Manufacture of knitted and crocheted hosiery 0·2901810 Manufacture of leather clothes 0·2031822 Manufacture of other outerwear 0·1812211 Publishing of books 0·178

Most dispersed

1520 Processing and preserving of fish and fish products 0·2003511 Building and repairing of ships 0·1131581 Manufacture of bread, fresh pastry goods and cakes 0·0942010 Saw milling and planing of wood, impregnation of wood 0·0822932 Other agricultural and forestry machinery 0·0671551 Operation of dairies and cheese making 0·0641752 Manufacture of cordage, rope, twine and netting 0·0623615 Manufacture of mattresses 0·0501571 Manufacture of prepared feeds for farm animals 0·0492030 Manufacture of builders’ carpentry and joinery 0·047

industries are also in the same list together with three media-based industries. These highlylocalizedindustries are fairly exceptional. In contrast, the mean industry (after ranking industriesby their degree of localization) is barely more localized than if randomly distributed. It is mostlyfood-related industries together with industries with high transport costs or high dependence onnatural resources that show dispersion.

Our main focus in this paper is on the proportion of manufacturing sectors that are localized.However, it is interesting to notice that a number of industries that appear inTable 2are fairlysmall in terms of overall employment. This raises the question as to whether the percentage ofmanufacturing workers employed in localized industries is above or below the percentage ofsectors that are localized. Weighting sectors by their share in manufacturing employment, wefind that 67% of U.K. manufacturing employers work in sectors that are localized. This showsthat localized sectors tend to have a larger share of manufacturing employment. Offsetting this,however, is the fact that the employment share weighted mean of the index of globalization,0A, is 30% lower than the unweighted mean of the index. That is, larger sectors tend to be lessstrongly localized.

Finally, it is also interesting to notice that for many (two-digit) branches, related industrieswithin the same branch tend to follow similar patterns.Table 3 breaks down localizationof industries by branches. For instance nearly all Food and Drink industries (SIC15) orWood, Petroleum, and Mineral industries (SIC20, 23 and 26) are not localized. By contrast,most Textile, Publishing, Instrument and Appliances industries (SIC17–19, 22 and 30–33) arelocalized. The two main exceptions are Chemicals (SIC24) and Machinery (SIC29). In thesetwo branches, however, the more detailed patterns are telling. Chemical industries such asFertilisers (SIC2415) vertically linked to dispersed industries are also dispersed whereas thoselike Basic Pharmaceuticals (SIC2441) or Preparation of Recorded Media (SIC2465) verticallylinked to localized industries are themselves very localized. The same holds for machinery: Other



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Particular IndustriesDURANTON & OVERMAN TESTING FOR LOCALIZATION 1093

TABLE 3

Localizationby two-digit branch

Two-digit branch Number of No. global No. globalfour-digit localization localizationindustries ≤60 km >60 km

15 Food products and beverages 30 1 016 Tobacco products 1 1 017 Textiles 20 16 918 Wearing apparel, dressing, etc. 6 6 319 Tanning and dressing of leather, footwear 3 3 320 Wood and products of wood, etc. 6 0 021 Pulp, paper and paper products 7 2 122 Publishing, printing and recorded media 13 13 823 Coke, refined petroleum products 3 0 024 Chemical and chemical products 20 8 825 Rubber and plastic products 7 1 326 Other non-metallic mineral products 24 4 227 Basic metals 17 11 1028 Fabricated metal products 16 9 1229 Other machinery and equipment 20 6 930 Office machinery and computers 2 2 231 Electrical machinery 7 2 532 Radio, televisions and other appliances 3 3 333 Instruments 5 3 434 Motor vehicles, trailers, etc. 3 1 335 Other transport equipment 8 2 236 Furniture and other products 13 4 5

Aggregate 234 98 92

Agricultural and Forestry Machinery (SIC2932) is very dispersed like most agriculture-relatedindustries,whereas Machinery for Textile, Apparel and Leather Production (SIC2954) is verylocalized like most textile industries.

5. ESTABLISHMENT SIZE AND LOCALIZATION

Four main conclusions emerge so far: (i) 52% of industries are localized, (ii) localization mostlytakes place at small scales, (iii) deviations from randomness are very skewed across industriesand (iv) industries that belong to the same branch tend to have similar localization patterns. Thesefindings may be driven by particular types of establishments or particular sectoral definitions. Togain insights about the size of localized establishments and the scope of localization, we replicateour analysis with alternative samples of plants and alternative sectoral definitions. This sectiondeals with size issues; questions relating to scope are examined in the next section.

Note that the issue of size may be particularly crucial as firm-size distributions arevery skewed in most industries. In our population of plants, 36% of establishments employtwo persons or less and represent only a very small fraction (2·4%) of total manufacturingemployment. The issue of firm size is also important from a policy perspective. Policiesencouraging dispersion are not likely to be very successful if it is only small establishments thatcan be dispersed, whereas clustering policies might be more difficult to implement if it is onlylarge establishments that cluster. Finally, the type of establishments, big or small, that cluster ordisperse is potentially very informative about the relevance of particular theories.



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Desmet and Rossi-Hansberg (2013)

Why do people live in particular cities? Agents canI be more productive (productivity advantages, high price of tradeables)I enjoy the city (amenities, geography)I frictions may be low (urban costs, taxes, infrastructure, other market frictions)

We use a simple urban theory to calculate these components for the U.S.economy

I "Wedge" analysis as in Chari, et al. (2007)I With and without externalities in productivity and amenities

Wide set of counterfactual exercises that explain the relative importance ofthese characteristics for welfare


Findings

We find that eliminating differences in any of these characteristics leads toI Small changes in welfareI Large population reallocations

Externalities have an overall small effect but lead to important city selection

The effect of productivity and amenity shocks is substantially reduced by theurban structure

Provide a simple methodology to compare urban systems across countriesI Illustrate using the cases of the U.S. and China


The Model

Standard model of a system of cities with:I Elastic labor supply so that labor taxes create distortionsI Nt identical agents choose where to live and workI Cities have idiosyncratic productivities and amenitiesI Mono-centric cities that require commuting infrastructures that citygovernments provide by levying labor taxes

I City governments can be more or less effi cient in the provision of the publicinfrastructure. We refer to this variation as a city’s excessive frictions.

Later add externalities in productivity and amenities


Technology

Goods are produced in I mono-centric circular cities with sizes NitCities have a local level of productivity Ait . Production in a city i in period tis given by

Yit = AitKθitH

1−θit

The standard first order conditions of this problem are

wit = (1− θ)YitHit

= (1− θ)yithit

rt = θYitKit

= θyitkit

Capital is freely mobile across locations so there is a national interest rate rtWe can then write down the “effi ciency wedge”which is identical to the levelof productivity, Ait , as

Ait =Yit

K θitH

1−θit

=yit

kθith1−θit


Preferences

Agents order consumption and hour sequences according to

∞

∑t=0

βt [log cit + ψ log (1− hit ) + γi ]

where γi denotes the amenities associates with city i

The problem of an agent with capital k0 is therefore

max{it ,cit ,hit ,kit}∞

t=0

∞

∑t=0

βt [log cit + ψ log (1− hit ) + γi ]

subject to

cit + xit = rtkit + withit (1− τit )− Rit − Titkit+1 = (1− δ) kit + xit ,

In steady state kit+1 = kit and xit = δkit . Furthermore, we assume kit issuch that rt = δ (capital is at the Golden Rule level)


The Labor Wedge

The simplified budget constraint of the agent becomes

cit = withit (1− τit )− Rit − Tit .

The first order conditions of this problem are given by

1cit= λit ,

andψ

11− ht

= wit (1− τit ) λit ,

So the labor wedge τ is given by

(1− τit ) =ψ

(1− θ)

cit1− hit

hityit


Commuting Costs and Land RentsCities are mono-centric, all production happens at the center, and people livein surrounding areas characterized by their distance to the center, d

Each agent lives on one unit of land and commutes from his home to work.Commuting is costly in terms of goods, T (d) = κd

We normalize the price of agricultural land to zero. Since land rents arecontinuous in equilibrium, R (d) = 0.

Since all agents in a city are identical,

Rit (d) + T (d) = T (dit ) = κdit

Hence

Rit (d) + T (d) = κ

(Nitπ

) 12

all d

Average land rents are equal to

ARit =2κ

3

(Nitπ

) 12


Government Budget Constraint and Frictions

The government levies a labor tax, τit , to pay for the transportationinfrastructure

I It requires κgit workers per mile commuted to build and maintain urbaninfrastructure. So

G (hitwit ,TCit ) = githitwitκTCit = githitwitκ23

π−12N

32it

I Hence, git is inversely related to the effi ciency of the government in providingurban infrastructure

I The government budget constraint is then given by

τithitNitwit = githitwitκ23

π−12N

32it

which implies that the “labor wedge” can be written as

τit = gitκ23

(Nitπ

) 12


Characterization of Equilibrium

Labor market equilibrium satisfies ∑Ii=1 Nit = Nt and all agents receive thesame utility level u

So given (Ait ,γit , git ) we can calculate Nit all i

In equilibriumI More productive cities are largerI Cities with larger amenities are largerI Larger cities have more frictions, but this tradeoff depends on how effi cientlocal governments are in providing urban infrastructure

F “Excess frictions” make cities smaller

We explore these derivatives using data on U.S. cities and paying attention tothe general equilibrium effects

I The empirical results are consistent with the theory


Testing the model with US data


Identifying City Characteristics

Need to calculate the triplet (Ait ,γit , git ) from the data

Obtain "effi ciency wedge" from

Ait =yit

kθith1−θit

I We can do this with or without capital data

Calculate "labor wedge" from

(1− τit ) =ψ

(1− θ)

cit1− hit

hityit

Then obtain ln git from

ln τit = α+12lnNit + ln git

Use model to obtain γit so as to match size distribution of cities with u = 10


Data

Data for all MSA in the U.S. between 2005-2008I Cities with population greater than 50 000, consistently measured after 2003

Consumption: No readily available data on consumption at MSA levelI Use retail earnings and adjust using national averagesI For housing consumptions use gross rents

Capital: use U.S. sectoral capital stocks and allocate it to MSAs according totheir shares in sectoral earnings

Hours worked: use Current Population Survey but eliminate MSAs with lessthan 50 observations

Housing rental prices: use American Community Survey


Parameters

Let ψ = 1.4841 and θ = 0.3358 as in McGrattan and Prescott (2009).

Let r = δ = 0.02 (assumptions on capital)

Useln τit = α+

12lnNit + ε5it

then we can identify κ from the estimate of α as the model implies. Weestimate κ = 0.0017

I We use κ = 0.002 but do robustness checks with other values of κ

If we eliminate all characteristics, welfare would increase by 3.26% and allcities would have 1 million 68 thousand people


The Effect of Kappa

10 11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Effect of given all Shocks

= 0.0005, Utility = 10.49 = 0.001, Utility = 10.31Actual: = 0.002, Utility = 10 = 0.004, Utility = 9.39 = 0.006, Utility = 8.79


Counterfactuals Without One Shock

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Model Utility = 10

Counterfactuals Without One Shock, = 0.002 , = 0 , = 0

ActualModeled

10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Counterfactual Utility = 10.1217, Reallocation = 0.367

ActualAvg. Efficiency

8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)


ActualAvg. Amenities

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)


ActualAvg. Exc. Frictions


Counterfactuals With Only One Shock

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Model Utility = 10

Counterfactuals with Only One Shock, = 0.002 , = 0 , = 0

ActualModeled

-5 0 5 10 15 20-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)


ActualEfficiency Only

8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)


ActualAmenities Only

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)


ActualExc. Frictions Only


Reallocation

Calculate reallocation following Davis and Haltiwanger (1992) by adding thenumber of new workers in expanding cities

I Same effi ciency: 37% reallocation and welfare gains of 1.2%Example: New York would lose 77% of its population

I Same amenities: 20% reallocation and welfare gains of 0.2%Example: San Diego would lose 42% of its population

I Same excessive frictions: 44% reallocation and welfare gains of 0.8%Example: Trenton would gain 326% of its population

So very large reallocations, but small welfare gainsI Reallocation in the U.S. economy amounts to around 2.1% over 5 years


Geographic Distribution Without Differences in Amenities: Without Differences in Efficiency:

Without Differences in Excessive Frictions:


Changing the Level of Excessive Frictions

11 11.5 12 12.5 13 13.5 14 14.5 15-6

-5

-4

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-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

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Excessive Frictions Counterfactuals: US

All Excessive Frictions at 90th Percentile, Utility = 9.2023All Excessive Frictions at 50th Percentile, Utility = 9.7505All Excessive Frictions at 10th Percentile, Utility = 10.1663

So overall cost of excessive frictions is significant in levels: Role for policy


Adding Production Externalities

LetAit = AitN

ωit

where Ait is an exogenous characteristic and ω governs the elasticity ofproductivity with respect to size

Fairly robust estimate of ω in the literature, so use ω = 0.02


Counterfactuals with Production Externalities

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Model Utility = 10

Counterfactuals Without One Shock, = 0.002 , = 0.02 , = 0

ActualModeled

8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)




Adding Externalities in Amenities

Letγit = γitN

ζit

where γit is an exogenous characteristic and ζ governs the elasticity ofproductivity with respect to size

I As in the case of production externalities we let ζ = 0.02

Reallocation and welfare changes very similar

Less dispersion of city characteristics tends to decrease utility in the presenceof externalities

City selection effect is stronger


Counterfactuals Without One Shock and Both Externalities

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Model Utility = 10

Counterfactuals Without One Shock, = 0.002 , = 0.02 , = 0.02

ActualModeled

8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)




With Externalities but Only Average Characteristics

6 8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Actual, Utility = 10No Shocks, = = 0.02, Utility = 9.991No Shocks, = = 0.04, Utility = 9.877No Shocks, = = 0.06, Utility = 9.703

For ω = 0.02, 131 cities with only 613 agents and 61 with 3320745


Comparing with China

12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Model Utility = 10

China: Counterfactuals Without One Shock, = 0.001 , = 0 , = 0

ActualModeled

8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)




Comparing with China

12.5 13 13.5 14 14.5 15 15.5 16 16.5-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Excessive Frictions Counterfactuals: China

All Excessive Frictions at 90th Percentile, Utility = 9.2718All Excessive Frictions at 50th Percentile, Utility = 9.8461All Excessive Frictions at 10th Percentile, Utility = 10.2043


Conclusions

System of cities in U.S. such that large changes in city characteristics (orpolicy) have small effect on welfare but large effect on reallocation

With externalities, city selection becomes an important part of reallocation

Implies that the losses from lack of mobility are likely smallI Small mobility costs would yield negative welfare effects

More generally: Paper provides a simple GE methodology to compare urbansystems

I Identify main characteristics of citiesI Understand the effect of shocks and policyI Assess magnitude of welfare gains at stake

F Small in the US, but much larger in China


Documents

Lecture 7: Industrial Concentration and Systems of Citieserossi/Urban/Lecture_7_538.pdf · Lecture 7: Industrial Concentration and Systems of Cities WWS 582a Esteban Rossi-Hansberg