Urban Accounting and Welfare - NUS · Urban Accounting and Welfare Klaus Desmet Universidad Carlos...

Urban Accounting and Welfare∗

Klaus Desmet

Universidad Carlos III

Esteban Rossi-Hansberg

Princeton University

Abstract

We use a simple theory of a system of cities to decompose the determinants of thecity size distribution into three main components: effi ciency, amenities, and frictions.Higher effi ciency and better amenities lead to larger cities but also to greater frictionsthrough congestion and other negative effects of agglomeration. Using data on MSAsin the United States, we estimate these city characteristics. Eliminating variation inany of them leads to large population reallocations, but modest welfare effects. Weapply the same methodology to Chinese cities and find welfare effects that are manytimes larger than those in the U.S.

1. INTRODUCTION

Why do people live in particular cities? We can list many reasons, but two are undoubtedly

relevant. Agents can enjoy the city or be more productive there. A combination of life

amenities and productivity levels determines the size of cities, but the positive effects of these

characteristics are capped by the costs and frictions arising from congestion. Depending on

city governance and the flexibility of markets, these costs and frictions can be more or less

important. These city characteristics are in turn enhanced and amplified by the presence of

urban externalities. Understanding the different forces that determine city sizes is crucial

for answering a broad set of questions. What is the relative importance of these forces in

determining the size distribution of cities? How much would we gain or lose if cities had

similar amenities, technology levels, or frictions? How much reallocation would this cause?

More generally, what are the welfare implications of the location of agents across cities?

In this paper we provide a simple way of decomposing the characteristics that lead to the

size distribution of cities into three main components: effi ciency, amenities, and excessive

frictions. We use a simple urban theory to calculate these components and to carry out a

wide set of counterfactual exercises that provide answers to the questions we asked above.

∗We thank Kristian Behrens, Gilles Duranton, Wolfgang Keller, Stephen Redding, Alessandro Lizzeri(the editor) and three anonymous referees for helpful comments, and Joseph Gomes and Xuexin Wang forexcellent assistance with the data. We also thank Jordan Rappaport for sharing some of the quality of lifedata. We acknowledge the financial support of the International Growth Centre at LSE (Grant RA-2009-11-015), the Comunidad de Madrid (PROCIUDAD-CM), the Spanish Ministry of Science (ECO2008-01300and ECO2011-27014) and the Excellence Program of the Bank of Spain.

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The theory consists of a multi-city model with monocentric cities that produce a single good.

Workers decide how much to work and where to live. Effi ciency is modeled as TFP, amenities

as directly affecting preferences, and frictions as the cost of providing urban infrastructure

that is paid for with labor taxes. To measure “excessive frictions,”we use the concept of a

“labor wedge”(see Chari, et al., 2007) and decompose it into the standard congestion effect

of city size and the cost of providing city services. A city’s “excessive friction”is the relative

level of this latter term. We then solve the general equilibrium model with and without

externalities.

We first use aggregate data and the corresponding implications of the theory to calibrate

all parameters. We then use the structure of the model to identify “excessive frictions”

and effi ciency levels across cities. Finally, we use the general equilibrium of the model to

determine the amenities that make cities be their actual sizes. Therefore, the model matches

by construction the size distribution of cities in the United States.1 To verify externally the

results of our identification strategy, which relies on the model’s structure and its functional

form assumptions, we compute correlations between the estimated amenities and a wide

variety of urban attributes that are frequently related to urban amenities, like climate,

quality of life, and geography. We also compare our estimates of effi ciency to measures of

wages and productivity, and our estimates of the labor wedge with a variety of proxies for

urban frictions like taxes, government expenditure, unionization, commuting costs, etc. The

results match well with the intuitive role that economists usually associate with these urban

characteristics. This match is relevant given that our identification relies on the functional

forms we use in the theory.

With the triplet of urban characteristics for each city in hand we perform a variety of

counterfactual exercises. The main exercise we focus on consists of eliminating differences

across cities in each of the three characteristics (effi ciency, amenities, or excessive frictions).

Our aim is two-fold. First, we assess the relative importance of the different characteristics

in determining the city size distribution. In that sense, the exercise parallels a growth

1Our empirical strategy uses data on output, consumption, capital, population, and hours worked but noinformation on housing prices or land rents. This has the advantage of reducing the data requirements toreproduce the exercise for other countries. However, the implied land values in our model do not necessarilymatch these prices in each city. In Section 3, we verify that the city characteristics we uncover are correlatedto average rents in the way our model predicts.

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(or business cycle) accounting exercise. Second, in the same way that the business cycle

literature is interested in understanding the welfare effects from smoothing shocks across

time, we are interested in quantifying the effect of smoothing city characteristics across

space. This is relevant for regional policy, which often aims to revamp backward regions by

making productive investments (increasing effi ciency), improving their attractiveness as a

place to live (increasing amenities), or improving local governance (excessive frictions).

For most counterfactuals we find that the changes in utility (and the equivalent changes

in consumption) are modest in spite of massive population reallocations. For example,

eliminating effi ciency differences across cities lowers equilibrium utility levels by a mere 1.2%,

and eliminating amenity differences reduces welfare by just 0.2%.2 When we account for

externalities, these numbers decline even further. The welfare implications of redistributing

agents across cities due to switching of any of the fundamental characteristics that account

for the actual size distribution are never greater than a couple of percentage points.3 This is

perhaps surprising given that the differences across cities in amenities and effi ciency levels can

be rather big,4 and given that the implied population reallocations can be as large as 40%.

Adding externalities has an important effect on the extensive margin in the counterfactual

exercises, with many cities exiting and the urban population settling in the surviving cities.

However, these externalities do not increase the welfare effects in the different counterfactual

exercises; if anything, the effects are even more modest.

A relevant question is whether the small welfare effects we uncover are inherent to the

model or specific to the U.S. To address this issue, we explore the same counterfactual

exercises for the size distribution of cities in China. We find welfare effects that are an order

of magnitude larger than in the U.S. For example, when eliminating effi ciency differences

across Chinese cities, welfare increases by 47%, compared to a corresponding 1.2% in the

2The magnitude of the welfare effects depends on the normalization of the level of utility in the originalequilibrium. In terms of consumption these welfare changes are equivalent to, respectively, a 12% and a 2%increase in consumption. Given the magnitude of the original changes, we view these magnitudes as modest,particularly when compared to the equivalent numbers in the case of China.

3This resembles the literature on business cycle accounting that found that eliminating business cycleswould lead to trivial effects (as in Lucas, 1987, we do not have the necessary distributional cost to obtainlarger losses as agents are identical, as emphasized by Storesletten et al., 2001).

4For example, the city with the highest productivity has more than 63% higher TFP than the city withmean TFP and 64% more than the median. Similarly, in the benchmark exercise, the range of amenitiesacross cities amounts to 12% of utility.

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U.S.

Beginning with Rosen (1979) and Roback (1982), there has been a large literature using

price data on rents and wages to infer differences in amenities and productivities across

cities. The research strategy derives from the theory of compensating differentials with

free mobility of individuals and firms across locations.5 A more recent literature exploits,

instead, the information content on quantity data to infer information on city characteristics

(Chatterjee and Carlino, 2001, Rappaport, 2007, Redding and Sturm, 2007). These papers

rely on employment or population data to back out location-specific amenity or productivity

parameters. In contrast to this previous work, which has at most heterogeneity in amenities

and productivity, our paper allows also for heterogeneity in excessive frictions.6 Furthermore,

none of these papers focuses on decomposing the role of the different city characteristics

in determining the city size distribution, and neither do they run counterfactual exercises

that assess the welfare implications. Our paper is also novel in that it provides a simple

methodology to compare urban systems across countries, as we do for the cases of China

and the U.S., where we find enormous differences with large welfare implications.

A few papers have structurally estimated models of city size distributions to run coun-

terfactual exercises. Related to our work is Au and Henderson (2006), who use a model

with agglomeration economies and congestion effects to analyze optimal city sizes in China.

After estimating their model, they calculate the welfare effects of migration constraints and

find that output per worker would increase substantially in some cities if labor were free to

move. However, different from us, they limit their attention to effi ciency and do not focus

on the other components determining city size. Also relevant is a recent working paper by

Behrens et al. (2011). It proposes a general equilibrium model of a system of cities that can

be compared with the data. In contrast to our work, their paper emphasizes pro-competitive

forces that work through firm selection to determine the productivity of cities. These forces

lead to trade between cities, and so their counterfactual exercises focus on how shocks in one

5See Albouy (2008) for a more recent application of this methodology.6Other work has emphasized the importance of frictions, productivity, and amenities in explaining the

distribution of city sizes. Glaeser et al. (2001), Glaeser et al. (2005), Albouy (2008), and Rappaport (2008,2009), for example, have underscored the importance of city amenities and institutional frictions. Othershave emphasized the importance of the relative effi ciency in production of the different urban areas (Holmesand Stevens, 2002, Holmes, 2005, Duranton and Overman, 2008) or the geographic characteristics of thelocations in which cities develop (Davis and Weinstein, 2002, Bleakley and Lin, 2012).

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city affect the distribution of population and productivities in other cities.

More broadly, our work also relates to the literature on the size distribution of cities, but

instead of taking a random growth approach in which city dynamics coming from productivity

or preference shocks determine the size distribution (as in Gabaix, 1999a,b, Duranton, 2007,

Rossi-Hansberg and Wright 2007, and Córdoba, 2008), we use a model to decompose the

individual city characteristics that lead to the cross-sectional distribution of city sizes. Since

our model has no mobility frictions or specific factors, agents move across cities as a response

to any temporary shock. In that sense, city dynamics play no role in our decomposition. Of

course, the measured levels of effi ciency, amenities or frictions may still be the result of these

dynamic mechanisms. To the extent that this is the case, our approach helps us assess the

contribution of particular dynamic factors to the distribution of city sizes.

The rest of the paper is organized as follows. Section 2 introduces a simple urban model

and explains the basic urban accounting exercise. Section 3 estimates a log-linear version of

the structural equations using U.S. data between 2005 and 2008 and obtains the reduced-

form effects of the three main characteristics of cities on rents and city sizes. Section 4

performs counterfactual exercises using the empirical values of these city characteristics.

Section 5 applies our methodology to China, and Section 6 concludes. Online Appendix A

shows how the population sizes of individual cities are affected when certain characteristics

change. Online Appendix B describes in detail the urban data set constructed.

2. THE MODEL

We use a standard urban model with elastic labor supply so that labor taxes create dis-

tortions. Agents work in cities with idiosyncratic productivities and amenities. They live in

monocentric cities that require commuting infrastructures that city governments provide by

levying labor taxes. Large cities are more expensive to live in because of higher labor taxes

and commuting costs but are large because of high levels of effi ciency or local amenities.

City governments can be more or less effi cient in the provision of the public infrastructure.

We refer to this variation as a city’s “excessive frictions.” In later sections we augment the

model to include local externalities in production and amenities.

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2.1 Technology

Consider a model of a system of cities in an economy with Nt workers. Goods are produced

in I monocentric circular cities. Cities have a local level of productivity. Production in city

i in period t is given by

Yit = AitKθitH

1−θit

where Ait denotes city productivity, Kit denotes total capital and Hit denotes total hours

worked in the city.7 We denote the population size of city i by Nit. The standard first-order

conditions of this problem are

wit = (1− θ) YitHit

= (1− θ) yithit

and rt = θYitKit

= θyitkit

(1)

where small-cap letters denote per capita variables (e.g. yit = Yit/Nit). Note that capital is

freely mobile across locations so there is a national interest rate rt. Mobility patterns will

not be determined solely by the wage, wit, so there may be equilibrium differences in wages

across cities at any point in time. We can then write down the “effi ciency wedge,”which is

identical to the level of productivity, Ait, as

Ait =Yit

KθitH

1−θit

=yit

kθith1−θit

. (2)

2.2 Preferences

Agents order consumption and hour sequences according to the following utility function

∞∑t=0

βt [log cit + ψ log (1− hit) + γi]

where γi is a city-specific amenity and ψ is a parameter that governs the relative preference

for leisure. Each agent lives on one unit of land and commutes from his home to work.

Commuting is costly in terms of goods.

The problem of an agent in city i0 with capital k0 is therefore

max{citt,hitt,kitt,it}∞t=0

∞∑t=0

βt [log cit + ψ log (1− hit) + γi]

7It would be straightforward to generalize this model to include human capital. We experimented withthis, and doing so did not substantially change any of the theoretical or empirical results.

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subject to

cit + xit = rtkit + withit (1− τ it)−Rit − Tit

kit+1 = (1− δ) kit + xit,

where xit is investment, τ it is a labor tax or friction associated with the cost of building the

commuting infrastructure, Rit are land rents and Tit are commuting costs (as we will see

below, Rit +Tit is constant in the city so the location of the agent’s home does not affect his

choices).8

Throughout the paper we assume that we are in steady state so kit+1 = kit and xit = δkit.

Furthermore, we assume kit is such that rt = δ (capital is at its Golden Rule level). The

simplified budget constraint of the agent becomes

cit = withit (1− τ it)−Rit − Tit. (3)

The first-order conditions of this problem imply ψ cit1−hit = (1− τ it)wit. Combining this

expression with (1), we obtain

(1− τ it) =ψ

(1− θ)cit

1− hithityit. (4)

As in Chari et al. (2007), we refer to τ ti as the “labor wedge.”Although τ ti is modeled as a

labor tax, it should be interpreted more broadly as anything that distorts an agent’s optimal

labor supply decision. Part of the labor wedge may be an actual labor tax, but another part

may reflect other distortions that act in the same way as a labor tax. As we show in Section

3.2 below, limiting ourselves to a strict tax interpretation risks missing a relevant part of the

distortions.

Agents can move freely across cities so utility in each period has to be determined by

u = log cit + ψ log (1− hit) + γi, (5)

for all cities with Nit > 0, where u is the economy-wide per period utility of living in a city.

8Since agents can move across cities, the subscript i depends on t, as written under the maximizationsign. To save on notation, we drop this additional subscript.

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2.3 Commuting Costs, Land Rents and City Equilibrium

Cities are monocentric, all production happens at the center, and people live in surrounding

areas characterized by their distance to the center, d. Cities are surrounded by a vast amount

of agricultural land that can be freely converted into urban land. We normalize the price

of agricultural land to zero. Since land rents are continuous in equilibrium (otherwise there

would be arbitrage opportunities), this implies that at the boundary of a city, dit, land rents

should be zero as well, namely, R(dit)

= 0. Since all agents in a city are identical, in

equilibrium they must be indifferent between where they live in the city, which implies that

the total cost of rent plus commuting costs should be identical in all areas of the city. So

Rit (d) + T (d) = T(dit)

= κdit for all d ∈[0, dit

],

since T (d) = κd where κ denotes commuting costs per mile.

Everyone lives on one unit of land, Nit = d2itπ, and so dit = (Nit/π)

12 . Thus, Rit (d) +

T (d) = κ(Nitπ

) 12 for all d. This implies that Rit (d) = κ

(dit − d

)and so total land rents in

a city of size Nit are given by TRit =∫ dit

0

(κ(dit − d

)d2π

)dd = κ

3π−

12N

32it . Hence, average

land rents are equal to ARit = 2κ3

(Nitπ

) 12 . Taking logs and rearranging terms, we obtain that

ln (Nit) = o1 + 2 lnARit, (6)

where o1 is a constant. We can also compute the total miles traveled by commuters in the

city, which is given by

TCit =

∫ dit

0

(d22π

)dd =

2

3π−

12N

32it . (7)

2.4 Government Budget Constraint

The government levies a labor tax, τ it, to pay for the transportation infrastructure. Let

government expenditure be a function of total commuting costs and wages such that

G (hitwit, TCit) = githitwitκTCit = githitwitκ2

3π−

12N

32it .

where git is a measure of government ineffi ciency. That is, the government requires κgit

workers per mile commuted to build and maintain urban infrastructure.9 The government9Note the simplifying assumption that maintaining and building infrastructure requires a certain number

of workers, not hours of work. The assumption simplifies the model since the number of hours does notappear in equation (8).

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budget constraint is then given by

τ ithitNitwit = githitwitκ2

3π−

12N

32it (8)

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

τ it = gitκ2

3

(Nit

π

) 12

(9)

or

ln τ it = o2 + ln git +1

2lnNit. (10)

Although as we mentioned before, the notion of a labor wedge is not limited to a strict

tax interpretation, here it is modeled as a tax that finances local infrastructure. However,

it is straightforward to write down an alternative model, in which τ it could be reinterpreted

as the fraction of time lost in commuting, that would lead to an equation similar to (10).

We choose not to do so, since that would oblige us to move away from the more tractable

monocentric city model.

2.5 Equilibrium

The consumer budget constraint is given by

cit = withit (1− τ it)−Rit − Tit = (1− θ) (1− τ it) yit − κ(Nit

π

) 12

.

To determine output we know that the production function is given by yit = Aitkθith

1−θit and

the decision of firms to rent capital implies that rtkit = θyit. Hence,

yit = Ait

(θyitrt

)θh1−θit = A

11−θit

(θ

rt

) θ1−θ

hit.

Using (4), we can derive

hit =1

1 + ψ

1 +ψ (Rit + Tit)

(1− θ) (1− τ it)

(rtθ

) θ1−θ

A1

1−θit

and

cit =(1− θ) (1− τ it)A

11−θit

(θrt

) θ1−θ − (Rit + Tit)

1 + ψ.

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The free mobility assumption in (5) implies that ut = log cit+ψ log (1− hit)+γit for some

ut determined in general equilibrium so

ut + (1 + ψ) log (1 + ψ)− ψ logψ (11)

= log

(1− θ)(

1− κgit2

3

(Nit

π

) 12

)A

11−θit(

rtθ

) θ1−θ− κ

(Nit

π

) 12

+ψ log

1−κ(Nitπ

) 12

(1− θ)(

1− κgit 23

(Nitπ

) 12

) ( rtθ ) θ1−θ

A1

1−θit

+ γit

The last equation determines the size of the city Nit as an implicit function of city produc-

tivity, Ait, city amenities, γi, government ineffi ciency, git, and economy-wide variables like rt

and ut. We can use this equation to derive the effect of the three city-specific characteristics

(Ait, γit, git) on Nit. First note that the LHS of (11) is decreasing in Nit. The LHS is also

increasing in Ait and γi and decreasing in git. Hence, we can prove immediately that

dNit

dAit> 0,

dNit

dγi> 0,

dNit

dgit< 0. (12)

So population increases in a more productive city or a city with more amenities, but it

decreases in a city with a less effi cient government.

The economy-wide utility level ut is determined by the labor market clearing conditionI∑i=1

Nit = Nt. (13)

This last equation clarifies that our urban system is closed; we do not consider urban-rural

migration.

3. EVIDENCE OF EFFICIENCY, AMENITIES, AND FRICTIONS

To lend validity to our theoretical model, we estimate the size of the three derivatives in

(12) and estimate the effect of land rents on population as in (6). When doing so, the general

equilibrium nature of the model will be key.

3.1 Empirical Approach

We first estimate the “labor wedge” using equation (4) and the “effi ciency wedge” in

equation (2). Note that the empirical measure of the “effi ciency wedge”is related not just

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to productivity but also to the relative price of city output. Although we have no way

of disentangling these two terms, in a theory with multiple goods, relative price effects

across cities would have isomorphic effects to changes in productivity. Hence, we just equate

productivity to our measure of the “effi ciency wedge.”

The general equilibrium nature of the model is important. For example, if we regress

the log of city size on the log of the labor wedge, we find a statistically significant positive

effect (coeffi cient of 1.2360 and p-value of 0.000). But it would be wrong to conclude that

higher frictions lead to greater city size. Rather, according to the theory, this positive

association would reflect more productive cities being larger, and larger cities experiencing

greater commuting costs. That is, in as far as greater commuting costs are due to cities being

more effi cient, they will be positively associated with city size. Only frictions “in excess”of

this basic trade-off between effi ciency and congestion will have a negative effect on city size.

In what follows we propose a methodology that accounts for these general equilibrium links

by decomposing these different effects.

We start by estimating the following equation

lnNit = α1 + β1 lnAit + ε1it. (14)

The value of β1 yields the effect of the “effi ciency wedge” on city population. According

to the model, β1 > 0 by (12). Furthermore, ln Nit (Ait) = β1 lnAit is the population size

explained by the size of the “effi ciency wedge.” In contrast, ε1it is the part of the observed

population in the city that is unrelated to productivity; according to the model it is related

to both git and γit. We can thus define the function ε1 (git, γit) ≡ ε1it.

Since the “effi ciency wedge” increases population size, total commuting increases, which

affects the “labor wedge”according to equation (10). This is the standard urban trade-off

between productivity and agglomeration. We can estimate the effect of productivity on the

“labor wedge”by using equation (10) and the decomposition of lnNit into ln Nit (Ait) and

ε1it provided by equation (14). Hence, we estimate

ln τ it = α2 + β2 ln Nit (Ait) + ε2it. (15)

According to equation (10), β2 > 0. That is, a city that is more productive and so has

more population will be more distorted. We denote the effect of effi ciency on distortions by

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ln τ it = β2 ln Nit (Ait). Equation (10) also implies that the error term ε2it is related to git

and to ε1 (git, γit) (since the labor wedge depends on all factors affecting population and not

just on ln Nit (Ait)). Hence, we define ε2 (git, ε1 (git, γit)) ≡ ε2it.10

We now use equation (6) to decompose the effect from all three elements of (Ait, γi, git).

To do so, we estimate

ln (ARit) = α3 + β3 ln τ it + β4ε1it + β5ε2it + ε3it (16)

using median rents for ARit. The model has clear predictions for β3, β4 and β5. In particular,

it implies β3 > 0, since by equations (6) and (12) effi ciency has a positive effect on population,

which has a positive effect on the level of distortions and on average rents. This is the

standard city size effect. The effects of γit and git are determined by the estimates of β4 and

β5. Note that ε1it and ε2it depend on both γit and git. However, since ε2it = ε2 (git, ε1 (git, γit))

depends only on γit through ε1it and we are including ε1it directly in the regression, β5 will

capture only the effect of changes in git on land rents. So, β5 captures the effect of git

on frictions and therefore average rents. Higher distortions imply a higher τ it. Hence, the

model implies that higher git, and therefore higher τ it and ε2it, implies lower population and

lower rents (see (12)). Thus β5 should be negative. Similarly, since we are controlling for

the effect of git by including ε2it, β4 will capture the effect of ε1it on land rents controlling

for git, which is the effect of γit on land rents, since ε1it = ε1 (git, γit) . Hence, the model

implies that β4 should be positive by equations (6) and (12). Our model implies that rents

are a non-linear function of (Ait, γi, git). In contrast, equation (16) assumes that it is a linear

function. Adding higher degree polynomials and interaction terms to this relationship can in

principle be important. We do so in our empirical implementation below, though this does

not affect results in any substantial way.

Note that we can then use equation (6) to relate average rents and population sizes. So

we estimate equation (6) as

ln (Nit) = α4 + β6 lnARit + ε4it. (17)

10Note that if we were to substitute for ln τ it and ln Nit (Ait) in equation (15) one obtains an equationthat includes yit and hit on the left- and right-hand side of the equation. This is standard when usinggeneral equilibrium frameworks. In our theory, this is not a problem when estimating β2 since productivityis exogenous. However, in practice, it might be the case that measurement error in yit and hit leads to anupward bias in the estimate of β2. We recognize this problem but point to the fact that aggregate output atthe city level is one of the better measured variables in our sample and it is measured directly by the BEA.

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According to the model, in a circular city, β6 = 2 > 0.

3.2 Effects of Effi ciency, Amenities and Frictions on City Size

To bring the model to the data, we construct a new data set on U.S. metropolitan statistical

areas (MSAs) for the period 2005-2008. Apart from output and rental prices, few ready-to-

use data are available at the MSA level. We rely on a combination of proxies previously used

in the literature and micro-data to come up with measures for the other relevant variables,

such as consumption, hours worked, and capital. Online Appendix B.1 provides details on

the construction of the data set and Table B.4 presents the data and the computed city

characteristics. Computing the “labor wedge”and the “effi ciency wedge”requires making

assumptions on the values of some parameter values. In particular we chose ψ = 1.4841 and

θ = 0.3358 to match aggregate moments as in McGrattan and Prescott (2010). We also set

r = δ = 0.02, a standard value for interest rates satisfying our assumption in Section 2.2.

Before implementing the empirical exercise of the previous section, it may be useful to

return to the discussion of what exactly the labor wedge is measuring. As we argued above,

the labor wedge is not just determined by taxes but by anything that distorts the optimal

labor decision of agents. Still, if taxes are part of what the labor wedge is, we would expect

the cross-city variation in taxes to be related to the cross-city variation in labor wedges. We

can decompose the labor wedge into taxes and other distortions such that

(1− τ it) = (1− τ ′it)(1− τ ith1 + τ itc

) (18)

where τ it is our measure of the labor wedge, τ ith is the labor tax rate, τ itc is the consumption

tax rate, and τ ′it are other distortions. Thus, we expect our measure of the total labor wedge,

(1 − τ it), to be correlated with (1 − τ ith)/(1 + τ itc). To explore this, we collect data on

labor taxes and consumption taxes at the MSA level and find a positive correlation of 0.27

(statistically significant at the 1% level). At the same time, we find that local taxes make up

on average 1/3 of the labor wedge. Therefore, although local taxes are positively correlated

with the labor wedge, an important part of the labor wedge consists of other distortions. At

the end of Section 4.1 we will discuss the correlation between the labor wedge and measures

of these other distortions in more detail.

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We now turn to the empirical exercise of the previous section. We pool the data for 2005-

2008 and include time dummies in all regressions. One further difference is that we also

include an interaction term ε1itε2it in equation (16), since we found it to be statistically highly

significant. We denote the coeffi cient associated with this interaction term β7. Standard

errors for equations (16) and (15) are obtained by bootstrapping, since some of the regressors

are estimated.11 The results are presented in Table 1.

Table 1

j βj12 s.e. P-value Theoretical Prediction

1 2.0964 0.3727 0.000 +

2 0.4127 0.0234 0.000 +

3 0.1283 0.0461 0.005 +

4 0.0959 0.0070 0.000 +

5 −0.2020 0.0420 0.000 −

6 2.1400 0.3824 0.000 2

7 −0.1841 0.0437 0.000 −

Number of obs.: 768

As is clear from Table 1, all coeffi cients have the signs implied by the model and are

highly significant. The estimation of equations (14), (15), (16), and (17) yields R2 values of,

respectively, 0.14, 0.37, 0.25 and 0.18. The model implies that in a circular city β6 = 2. The

value we find is close to two and we fail to reject the hypothesis that it is equal to two at

the 5% level.

These results allow us to reach several conclusions. First, highly effi cient cities are more

populated. This is consistent with numerous empirical studies in the literature. Second,

effi cient cities are more distorted. Frictions are larger as a result of these cities being larger.

The frictions that result frommore effi cient cities being larger are positively related to median

rents, since they are the result of the higher effi ciency. Third, frictions that exceed the ones

11Correcting the standard errors for clustering by MSA does not qualitatively change any of the results,except for β3, which is no longer statistically significant.12The coeffi cients refer to the estimates of lnNit = α1 + β1 lnAit + ε1it, ln τ it = α2 + β2 ln Nit (Ait) + ε2it,

ln (ARit) = α3+β3 ln τ it+β4ε1it+β5ε2it+ε3it, and ln (Nit) = α4+β6 lnARit+ε4it, as explained in Section3.1.

14

explained by effi ciency have a negative effect on land rents and city size. Finally, cities that

are larger due to amenities also exhibit larger median rents.

The model and the empirical exercise have allowed us to assess the impact of the three city

characteristics (effi ciency, excessive frictions, and amenities) on land rents and population

size. It has also made the point that the general equilibrium effects are important. However,

the empirical log-linear model that we have used does not inherit the entire structure of the

model. For example, the derivatives in (12) need not be constant. It is therefore important

to go beyond this simple empirical exercise to capture the full richness of the theoretical

model. In the next section we propose a methodology to obtain the value of the three key

city characteristics, and we use the model to perform counterfactual exercises. We show how

the model can be made to account for all of the variation in city sizes if we identify amenities

as a residual from the theory.

4. COUNTERFACTUAL EXERCISES

In this section we start by showing how to identify the different city characteristics (effi -

ciency, amenities, and frictions) and then run a number of counterfactual exercises. Initially

we focus on the benchmark case without externalities, as this helps lay out the basic work-

ings of the model. We later extend the model to the more realistic case of local externalities

in production and amenities. The role played by externalities can then easily be uncovered

by comparing the results with the benchmark case.

4.1 Methodology and Identification of City Characteristics

The model provides a straightforward way of performing counterfactual exercises. Equa-

tion (11) implies that

C1 (ut, γit)− log (C2 (Ait, rt))

= (1 + ψ) log

(1−

(κ

2

3git +

κ

C2 (Ait, rt)

)(Nit

π

) 12

)− ψ log

(1− κ2

3git

(Nit

π

) 12

),

where

C1 (u, γit) = ut + (1 + ψ) log (1 + ψ)− ψ logψ − γit, and C2 (Ait, rt) = (1− θ) A1

1−θit(

rtθ

) θ1−θ

.

15

If git and τ are small using the approximation log (1− x) ≈ −x,13 we obtain

Nit =π

κ2

(log (C2 (Ait, rt))− C1 (u, γit)

(1+ψ)C2(Ait,rt)

+ 23git

)2

. (19)

Note that the approximation results in exactly the same derivatives with respect to (Ait, γit, git).

Furthermore, ∂Nit/∂u < 0, namely, a higher equilibrium utility (smaller total population)

makes concentration of workers in a given city less likely since concentration implies conges-

tion costs.14

We can use the equation above to calculate Nit given the values of (Ait, γit, git) and other

parameter values. We can also use these expressions to run counterfactual exercises. In

particular we can calculate counterfactual distributions of city sizes assuming that all cities

have similar values of any of the exogenous city characteristics (Ait, γit, git). Note that ut has

to be selected such that the resulting city sizes satisfy the labor market clearing condition

(13). In order to perform any of these exercises we first need to develop a strategy to calculate

(Ait, γit, git) for each city. Ait = yit/kθith

1−θit can be calculated directly from available data on

yit, hit and kit.15 Obtaining values for the other two city characteristics is more complicated.

First note that equation (10) can be used to estimate git. Based on this equation we can run

the simple log-linear regression

ln τ it −1

2lnNit = α5 + ε5it. (20)

We use data for 2005-2008 and add time dummies. Equation (10) then implies that ε5it =

13This approximation works best if τ it and κ are small. In the exercise below the approximation error islikely very small.14Throughout this section we calculate an agent’s utility based on his labor and capital income but not on

the income he obtains from land rents. Land is owned by absentee landlords and so rental income does notenter an agent’s utility and does not affect his decision to move. We have calculated all of the results below ifwe use the alternative assumption that workers in a city own a diversified portfolio of land in the city and soobtain as income the average rents. The results under this assumption are essentially identical (utility differsonly by less than 0.001) to the ones with absentee landlords, both in the case with and without externalities.The reason is that we are always normalizing the level of utility that reproduces the size distribution tou = 10 and only relative utilities matter to determine location decisions.15This is what we did in the empirical implementation above. An alternative way of calculating the relevant

productivity term without using kit (which is potentially poorly measured in the data) is to use the predictionof the model on capital allocation. In particular the model implies that kit = θyit/rt. Equation (19) assumesthat capital is determined in this way and so this method has the advantage of being theoretically moreconsistent (although it does not use the actual data on capital stocks). We have added capital in bothways and found the results to be similar. The correlation of the model-based capital stock measure and theempirical capital stock measure is 0.9. Therefore, we omit here the exercise with the theoretical levels ofcapital and focus on the one where we use the empirical measure of the capital stock.

16

ln git.16 Note that since in expression (9) both κ and git enter multiplicatively we can only

identify ln git relative to the constant α5 (which includes the unknown parameter κ) by

imposing that the mean of ln git is 0. This explains why we refer to this city characteristic as

“excessive frictions.”That is, it measures the frictions over and above what city size would

predict. To be clear, we are identifying git by attributing the variation in τ it after controlling

for city size, Nit, to git, but the level of this relationship is attributed to the transport cost

parameter κ as we explain below.

We still have to obtain the value of γit. There are a variety of ways to do this. The one

that is most consistent with the theory is to use equation (19) and solve for the set of γit that

makes the model match city sizes exactly, given some normalization of u (we set u = 10).

We can then fix γit and perform counterfactual exercises. Of course, this exercise depends

on the value of all parameters in the model. We use the same parameters used above. One

extra important parameter in determining γit is κ, for which we have not assigned a value

yet. To obtain a value for κ, notice that equation (9), together with regression (20), implies

that

α5 = ln

(2

3

)+ lnκ− 1

2ln π

and so, given a value for α5 from regression (20), we can calculate κ. The estimation gives

a value of κ = 0.002. The time dummies we include are mostly not significant, and their

values are so small that adding them would not change the value of κ.

Given that our identification strategy of the different city characteristics depends on the

model’s structure (and its functional form assumptions), it might be interesting to compare

our estimates with common empirical direct measures of these characteristics. This is espe-

cially true for the amenities, which are not directly measured, but estimated as the residual

that makes the model match the observed city sizes. We follow the quality-of-life literature

(see, e.g., Rappaport, 2007) and collect data on climate (such as average low temperature in

January, annual precipitation, annual precipitation days, and July heat index), proximity to

water (oceans, Great Lakes and major rivers), and other life-quality measures from different

city rankings (such as transport, education, health, crime, arts, recreation and leisure). As

16Alternatively, we could run ln τ it = α5 + β8 lnNit + ε5it. This is the same as (20) without restrictingβ8 to be equal to 1/2. Using effi ciency as an instrument for population, we find β8 = 0.4, similar to the 0.5predicted by the theory.

17

can be seen in Table B.1 in Online Appendix B, of the 23 correlations between our estimates

of amenities and these alternative measures, 22 have the expected sign, of which 18 are

statistically significant at the 10% level. As for effi ciency, we likewise find a strong positive

correlation between our effi ciency measure and wages (0.79) and labor productivity (0.90).

See Table B.2 in Online Appendix B.

Finding measures of frictions that can be directly related to labor wedges or excessive

frictions is harder. As we have emphasized above, excessive frictions can be related to taxes,

commuting costs, excessive government expenditures given the magnitude of infrastructure

projects, as well as other labor market or land use frictions. Importantly, some of these

frictions are fundamental and will cause cities to be small, while others will just be the

result of congestion in larger, and more complex, cities. In principle, fundamental sources

of frictions should be correlated with our measure of excessive frictions, while the actual

observed frictions should be related to the labor wedge τ . We attempted to disentangle the

impact of g and τ empirically in Section 3. Here, given that our measures of frictions are

all observed outcomes at the city level and not underlying sources of frictions, we correlate

these measures with the labor wedge τ . Table B.3 in Online Appendix B presents the

results. Of the 11 correlations, 10 have the right sign and 8 are significant at the 5% level.

Land use regulation does not seem to be related to our notion of frictions and public sector

unions are not statistically significant, although private ones are. Taxes, local expenditures

and commuting costs are all positively and significantly related to the labor wedge as well.

Overall, the comparison of our three city characteristics with standard direct measures seems

to suggests that our identification strategy yields city characteristics that can be interpreted

in standard ways.

4.2 Counterfactuals

We are now ready to perform a number of counterfactual exercises. After analyzing the

effect of commuting costs, the main focus will be on exploring the relative importance of

different characteristics (effi ciency, amenities and excessive frictions) in determining the city

size distribution. In particular, we are interested in understanding how changes in city

characteristics affect city sizes, welfare and the reallocation of people.

18

10 11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

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

Figure 1: The City Size Distribution for Different Levels of Commuting Costs

Figure 1 shows the actual distribution of city sizes in the U.S. and counterfactual distri-

butions of city sizes if we increase or decrease commuting costs κ, given the distribution of

characteristics. The results are presented in the standard log population — log rank plots

in which a Pareto distribution would be depicted as a line with slope equal to minus the

Pareto coeffi cient. As is well known, the actual distribution is close to a Pareto distribution

with coeffi cient one. By construction the model matches the actual distribution exactly for

κ = 0.002. In all exercises we normalize the benchmark utility u = 10. This normalization

implies that the difference in utility from living in the city with the highest amenities relative

to the one with the lowest amenities amounts to 11.7% of utility. In all counterfactual exer-

cises we solve for the value of u for which the labor market clears, i.e., the sum of population

across cities equals the actual total urban population.17

17One of the goals of the counterfactual exercises is to quantify the welfare effects of different changes.Given that we have a log utility function in consumption, the normalization of the benchmark utility to 10implies that a 1% increase in utility is equivalent to a 10% increase in consumption. Both measures aresomewhat arbitrary. On the one hand, it is unclear what a 10% increase in consumption means in terms ofwelfare if utility depends on many other factors like leisure and the quality of life in a city. On the otherhand, the effect in terms of utility depends on the arbitrary normalization. Subject to these caveats, the

19

As can be seen in Figure 1, larger commuting costs make the largest cities smaller and

the smaller cities larger, leading to a less dispersed distribution of city sizes. Doubling

commuting costs decreases utility by about 6.1%. Production moves away from the larger

and most productive cities, which leads to welfare losses. Halving commuting costs increases

dispersion and raises utility by 3.1%. Note that the smallest cities now become much smaller.

The main advantage of some of these cities was their small size and their corresponding low

level of congestion. As commuting costs decrease, this advantage becomes less important

and their size decreases further.

Figure 2 shows three counterfactual exercises where we shut down differences in each

of the three city characteristics (effi ciency, amenities, and excessive frictions), respectively.

In all cases we eliminate differences in a particular characteristic by setting its value to

the population weighted average. We then calculate the utility level that clears the labor

market, so total urban population is identical in all cases. Note that smoothing out spatial

differences always leads to an increase in utility. Differences create dispersion in the city size

distribution and by equation (7) total commuting costs are convex. So utility in the model

tends to increase if population is more evenly distributed in the 192 cities in our sample. If

we eliminate differences in all three components so that all sites are identical, welfare would

increase by 1.54% and all cities would have a population of 1 million 68 thousand people. Of

course, this increase in welfare does not constitute an upper bound, since the distribution of

the different city characteristics, as well as their correlation, matters for the final results.

The counterfactual exercises in Figure 2 show that eliminating differences in effi ciency,

amenities or excessive frictions has a modest effect on utility. In all cases utility would

increase by less than 1.5%. The limited effect on utility is due to several reasons. The

most obvious one is that population can reallocate across cities. But there are others. For

example, the effect of a negative shock to productivity on utility is also mitigated by people

working less, by lowering the cost of providing city infrastructure, and by the fact that utility

does not only depend on production but also on amenities. In as far as regional policies aim

rest of the paper maintains the focus on utility, with the understanding that any percentage difference inutility should be multiplied by 10 in order to transform it into a percentage difference in consumption. Ofcourse, in as far as relative statements are concerned, such as when we compare the U.S. and China, thereis no difference between both ways of expressing welfare differences.

20

to reduce differences in, say, effi ciency or amenities across space, these results suggest that

their effect on welfare is likely to be modest.

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

Model Utility = 10

ActualModeled

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

Counterfactual Utility = 10.1217, Reallocation = 0.367

ActualAvg. Efficiency

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)


ActualAvg. Amenities

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)


ActualAvg. Exc. Frictions

Figure 2: Counterfactuals Without Differences in One City Characteristic, κ = 0.002

In spite of the small effect on utility, the effect on the size of individual cities is large. In

the case of excessive frictions this is clear from Figure 2. Eliminating differences in excessive

frictions tends to hurt larger cities and benefit smaller ones: New York and Los Angeles

would lose up to 90% of their populations, whereas Santa Cruz and Trenton would gain,

respectively, 145% and 326%.18 This suggests that larger cities have been successful, not

just because of higher effi ciency but because they have been able to eliminate barriers and

other frictions that hinder growth. However, there are notable exceptions: the population

18Whenever we mention city names, we are referring to the MSA. For example, Los Angeles refers to LosAngeles-Long Beach-Santa Ana and New York refers to New York-Northern New Jersey-Long Island.

21

of Buffalo, a fairly large metropolitan area, would increase by 36% if differences in excessive

frictions were eliminated.

Although perhaps less obvious from Figure 2, equalizing effi ciency or amenities also has a

large effect on the size of individual cities. Larger cities would typically decline in size if they

had average levels of effi ciency. For example, Los Angeles would lose 29% of its population.

The respective figures for New York and Chicago would be losses of 77% and 46%. When

equalizing amenities, the picture is more mixed. One pattern that emerges is that many

East Coast cities would gain, whereas many West Coast cities would lose. For example,

New York and Philadelphia would increase their populations by 44% and 39% if differences

in amenities were eliminated, whereas Los Angeles and San Diego would lose 8% and 42%

of their populations. One would expect that equalizing effi ciency or amenities would tend

to benefit smaller cities. This is indeed sometimes the case – for example, the population

of Fargo would increase by 183% if its amenities were equal to the average – but by no

means always. Some of the smaller cities decline because they lose their only comparative

advantage. One such example is Santa Fe: if it had average amenities, it would lose 82% of

its population. Intermediate-sized cities often benefit as they tend to experience a boost in

productivity or amenities and are already attractive enough in terms of other characteristics.

These cities also grow because of the reallocation of population from larger cities.

Online Appendix A shows figures and maps with the percentage changes in population

for individual cities when we set one of the city characteristics to its weighted average. In

terms of the geographic distribution of city characteristics, we find that most cities on the

West Coast and in Florida would lose population if we eliminated amenity differences. This

is consistent with Rappaport and Sachs (2003) and Rappaport (2007), who argue that the

concentration of population in coastal areas with nice weather has to do increasingly with a

quality-of-life effect. Central regions would tend to lose population if we eliminated effi ciency

differences, as would most of the northeastern regions. Perhaps the sharpest geographical

pattern emerges when we eliminate excessive frictions. Many of the “Rust Belt” cities in

the Midwest and the Northeast would gain population if we equalized frictions across cities.

Examples include Rochester (+37%), Syracuse (+120%), Milwaukee (+16%), Allentown-

Bethlehem (+14%), and Toledo (+108%). This is an indication that governance problems,

22

as well as other labor market frictions, like unions, may be important in these places.

The effect of the different city characteristics on the distribution of city sizes hides some

of the implied population reallocation in these counterfactuals. That is, cities are changing

ranking in the distribution even if the overall shape of the distribution does not always

exhibit large changes, as in the case of amenities or effi ciency. We can calculate reallocation

following Davis and Haltiwanger (1992) by adding the number of new workers in expanding

cities as a proportion of total population when we change from the actual distribution to the

counterfactual. This measure of reallocation is 37% when we eliminate differences in TFP,

20% when we eliminate amenities, and 44% when we eliminate excessive frictions: large

numbers given the modest welfare gains. As a benchmark, the same reallocation number for

the U.S. economy over a 5-year interval is around 2.1% (over the period 2003-2008).

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

Model Utility = 10

ActualModeled

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)


ActualEfficiency Only

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)


ActualAmenities Only

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)


ActualExc. Frictions Only

Figure 3: Counterfactuals with Differences in Only One City Characteristic, κ = 0.002

23

Figure 3 shows the counterfactual distributions of city sizes when we equalize two of the

three characteristics across cities. The distributions therefore show the heterogeneity in

city sizes generated by a single characteristic. Note that neither effi ciency on its own nor

amenities on their own can explain the relatively large sizes of both the smallest and the

largest cities in the actual distribution. This is because some of these cities are attractive

in terms of their other characteristics, making them larger than their effi ciency or their

amenities on their own would imply.

11 11.5 12 12.5 13 13.5 14 14.5 15-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

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

Figure 4: Changing the Level of Excessive Frictions

Figure 4 shows a counterfactual exercise when we set excessive frictions in all cities equal

to the 10th, 50th or 90th percentile of the distribution of excessive frictions. First note

that just eliminating the variation in excessive frictions across cities and setting them at the

median decreases welfare by 2.5%. The figure shows that reducing frictions in all cities to

the 10th percentile increases the dispersion of city sizes. Large cities gain the most in terms

of population from the change, and many small cities exit. Utility increases by 4.2% relative

to setting the level of frictions at the median. An opposite effect results from setting frictions

to the 90th percentile, although the changes in the distribution are in general smaller. In this

24

case utility declines by 5.5% relative to the case where excessive frictions are at the median.

An increase in excessive frictions makes large cities particularly expensive since large cities

use the commuting technology more intensively (as we discussed in Section 2.4). As a result,

the economy produces in more uniformly sized cities and so fails to exploit the differences

in effi ciency and amenities across cities. This leads to a considerable change in utility.

4.2.1 Robustness Exercises.–

To assess the robustness of our results, we do a number of additional exercises. A first

robustness check concerns the elasticity of commuting costs relative to population. Our the-

oretical model assumes that population density is independent of size, implying an elasticity

of commuting costs relative to population of 0.5. It is straightforward to generalize the model

to allow for the possibility of larger cities being more dense.19 By regressing the log of area

on the log of population, we can then easily derive the implied elasticity. Depending on the

definition of a city (MSA vs. incorporated places with a population of more than 100,000),

we find a value of 0.25 or 0.5, respectively. Our theoretical value is therefore within the

range of plausible values. To evaluate whether an elasticity of 0.25 would overall be more

consistent with external data, we once again compute correlations between the estimated

amenities and the observed amenities, based on climate, life quality, and proximity to water,

and find a much worse fit than in the case of an elasticity of 0.5.20

It is nevertheless instructive to redo our basic counterfactual exercise in Figure 2 for an

elasticity of 0.25 (and the corresponding higher value of κ = 0.048, since κ depends negatively

on the elasticity). Recall that with an elasticity of 0.5 differences in excessive frictions have

a relatively large effect on the city size distribution, compared to differences in amenities

or effi ciency. In that case it is costly for cities to be large and so the ones that become

big must have very low excessive frictions. In contrast, when we drop the elasticity to 0.25,

19Consider a city in which population density increases with population size according to Nξ, wherexi ≥ 0. Then population in the city is given by Nit = d2itπN

ξit. Since d

2itπ is the area of the city, we can

use this equation to estimate ξ using data on area and population. Average commuting costs are given byACit = 2

3κπ− 12N

(1−ξ)/2it , so the elasticity of commuting costs to population is equal to (1− ξ) /2. So in the

monocentric city model with constant density, where ξ = 0, this elasticity is equal to 1/2.20With an elasticity of 0.25, of the 23 correlations computed, only 12 have the right sign, of which only 10

are statistically significant at the 10% level. This is a substantially worse outcome than with an elasticity of0.5.

25

becoming large is less costly, so that big cities no longer require excessive frictions that are

that low. The cross-city dispersion in excessive frictions therefore declines. But if so, the

dispersion in amenities must increase in order for the model to be able to account for the

actual city size distribution. So amenities play a larger role in determining the shape of the

size distribution of cities, and as a result, eliminating differences in amenities yields larger

welfare gains (4.2%). Equalizing excessive frictions also leads to larger gains (13.6%) since in

the case of a lower elasticity we are penalizing large cities much less by setting their excessive

frictions to the average level. The welfare gains from equalizing effi ciency decrease to 0.64%.

We present the results of this exercise in Figure A9 in Online Appendix A.

Since we have repeatedly argued that the labor wedge is about more than taxes, a second

robustness check analyzes whether our results change when we define the labor wedge as

being only due to distortions other than taxes. Following the same decomposition as in

(18), we now define the labor wedge as only the part that is due to “other distortions.”The

results are largely unchanged: the shapes of the counterfactual city size distributions are very

similar to the benchmark exercise. The only slight difference is that the welfare effects are

slightly larger when eliminating differences in effi ciency (1.9% instead of 1.2%) or amenities

(0.5% instead of 0.2%), and slightly smaller when eliminating differences in excessive frictions

(0.7% instead of 0.9%). This is easily understood: by considering only the part of the labor

wedge which is due to “other frictions,”the cross-city variation in labor wedges is reduced

and, with it, the cross-section variation in excessive frictions. Since differences in excessive

frictions therefore play less of a role in explaining the city size distributions, differences in

effi ciency and amenities must play, in relative terms, more of a role. As a result, eliminating

differences in excessive frictions has a slightly smaller welfare effect, whereas eliminating

differences in effi ciency and amenities has a slightly larger welfare effect.

A third robustness check concerns the level of commuting costs κ, which we have estimated

to be equal to 0.002. The larger κ, the smaller the relative importance of productivity

differences, since it becomes more costly to live in large productive cities and the people that

live in them tend to work less since τ is larger. If we set κ = 0.006, a threefold increase,

the total reallocation if we equalize effi ciency across locations drops from around 37% to

12%, with a 0.7% increase in utility, half of the effect we had with κ = 0.002. Reallocations

26

decrease from 20% to 8.5% when cities have average amenities, and utility now goes up by

0.3%, instead of by 0.2%. The reallocation if we set excessive frictions to their average level

remains essentially constant at 43%. The changes in city sizes are highly correlated in the

exercises with the two different values of κ.

A final robustness check studies the role retirees play in our calculations. Our measure of

average hours worked is affected by the distribution of retirees across cities. In particular,

cities with many people older than 65, many of whom do not work, appear very distorted

since labor supply per person is low. Of course, distorted cities in turn attract agents who do

not want to work, and so there are good arguments to include all agents in our calculation of

hours worked. Still, it is useful to assess the extent to which our results are driven by retirees

rather than active agents deciding on how many hours to work. For this purpose we redo our

main exercise excluding agents older than 70, or older than 65, from the calculation of hours

worked. All the main results remain unchanged and the quantitative impact of retirees is in

general small. So retirees do not drive our conclusions. Figure A10 in Online Appendix A

presents these results. Not including older agents has the largest impact when we eliminate

differences in effi ciency across cities. The reason is that retirees go to cities that have high

amenities but are not necessarily very productive. Excluding them increases hours worked

in those cities. This lowers measured productivity, thereby increasing dispersion in effi ciency

across cities.

4.3 Adding Production Externalities

So far we have taken productivity in a particular city to be exogenously given. We have

assumed that the effi ciency of a particular site is not affected by the level of economic activity

at that site. That is, so far effi ciency has explained agglomeration, but we have assumed

away the reverse link by which agglomeration explains effi ciency. Of course, a standard view

in urban economics suggests that agglomeration is, at least in part, created by an increase

in productivity coming from a rise in the number of people living in a given city. Including

these agglomeration effects in our calculations has the potential to change our results, as

this will have an endogenous effect on the size of a city.

To incorporate these effects, we start with equation (19) but recognize that the term Ait,

27

which captures the effi ciency of city i, is a function of the size of the city Nit. In particular,

we now let

Ait = AitNωit . (21)

That is, the level of productivity is now a function of exogenous productivity Ait, and city

size, Nit, where the elasticity of the effi ciency wedge with respect to population is given by

ω. Note that externalities operate within cities, and not across cities. We can then use the

previous calculation of effi ciency wedges, using equation (2), and divide by population raised

to ω. The result is a set of new exogenous effi ciency levels Ait. We then substitute (21) in

(19) and solve for the γit’s that yield the city’s exact population levels. Excessive frictions

are calculated as before. With all the city characteristics in hand, we now perform the same

set of counterfactual exercises as before. Note that equation (19) now includes Nit in the

productivity terms and so cannot be solved analytically. But we can solve the system of

non-linear equations numerically to obtain city sizes in the counterfactual exercises.

We still need to determine a suitable value for ω. Of course, the estimation of equation

(14) is not useful to determine ω. In fact, this equation will fit exactly as in the data in

our simulation of the actual economy. Instead, we rely on the literature, which suggests a

fairly robust estimate of ω = 0.02 (see, among others, Carlino, et al., 2007, and Combes,

et al., 2012). We therefore start with an initial value of 0.02 and perform some robustness

checks. We also set κ = 0.002 as estimated in the previous section. Clearly, allowing

for production externalities reduces the dispersion in exogenous effi ciency since the high

endogenous effi ciency of large cities is now largely due to their size, rather than to their high

exogenous effi ciency. For example, the exogenous effi ciency of Los Angeles, which we had

estimated to be 9% above the country’s average in the absence of externalities, now drops

to being 5% below the average once we allow for externalities.

Figure 5 presents the exercise with externalities in the case where we eliminate each

characteristic individually. First note that when we eliminate one of the characteristics,

small cities tend to become a lot smaller and some no longer survive. We use a cutoff of

log(8) to determine the cities that exit, which implies that cities become towns with about

3,000 people. The smallest MSA in our sample has a population of 129,000. In particular,

15 cities exit when we equalize Ait across cities to its population weighted mean, 29 cities

28

exit when we set amenities to their average value, and 6 cities exit with average excessive

frictions. As in the case without externalities, these are cities that lose their only comparative

advantage. With externalities, this loss gets compounded, leading some small cities to exit.

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

Model Utility = 10

ActualModeled

8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)ln

(pro

b >

popu

latio

n)



8 10 12 14 16 18-6

-5

-4

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-2

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ln(population)

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> po

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tion)



11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)



Figure 5: Counterfactuals Without Differences in One City Characteristic and

Externalities, κ = 0.002, ω = 0.02

Including externalities implies that large cities tend to become a lot smaller when elim-

inating differences in excessive frictions, whereas their size does not change much when

equalizing exogenous effi ciency or amenity levels. This latter result can be explained by

the smaller dispersion in exogenous effi ciency or amenities. Comparing this case to the one

without externalities, utility can increase or decrease. On the one hand, introducing ex-

ternalities reduces the underlying differences across cities, implying utility gains because of

convex commuting costs. On the other hand, differences in city characteristics allow cities

29

to exploit external effects, implying utility losses when making cities more alike. As a result

of these opposing forces, utility is virtually unchanged, relative to the case without exter-

nalities. Introducing externalities slightly increases the total reallocation required in the

counterfactuals. Compared to the case without externalities, the total reallocation required

in the counterfactual tends to go slightly up. This happens because the changes introduced

by the elimination of these characteristics get compounded through the effect of changes in

population on effi ciency.

Doubling the externality to ω = 0.04, closer to the estimate reported by Behrens et al.,

(2010), exacerbates the effects described above. More cities either exit or become very small.

The results suggest that selection of cities in the presence of externalities can be important.

Relative to the case without externalities, the increase in externalities does not significantly

change the utility gains obtained if we equalize one of the city characteristics.

Adding externalities in production implies that the equilibrium allocation we compute

is no longer effi cient. In contrast to the exogenous productivity case, city planners could

improve on the equilibrium allocation by subsidizing urban agglomeration. We can compute

the optimal allocations in the case with production externalities by letting a representative

firm internalize the external effect on productivity. Since the differences in welfare between

the cases with and without externalities are so small, it is not surprising that the effect

of these optimal urban policies is necessarily small as well. In fact, the gain in utility is

only 0.58%. Given that the informational requirements for these urban policies is extremely

high, it is not clear that actual policy can achieve these small gains. Figure A11 in Online

Appendix A compares the optimal and actual allocations.

We should also mention here that the exercise with externalities leads to the possibility

of multiple equilibria in the size of cities. For many cities it will be the case that, given the

equilibrium utility level, there is only one equilibrium size. But for other cities there may be

several possible equilibrium sizes. Our theory does not provide a way of selecting between

these equilibria so we always present the one that requires less reallocation. That is, we

always initialize the search for a solution of the size of a city at its actual size.

30

4.4 Adding Externalities to Amenities

We can also add externalities in the amenities a city provides. That is, we can let the

utility from living in a particular city depend on the size of the city directly. People live

in New York because living around a large number of people leads to a scale that provides

them with a variety of goods and services, and interactions with people, which they enjoy.

We have modeled the preference to live in a particular city through the amenity γit. So we

can simply let γit = γitNζit, where now γit is the exogenous amenity and ζ is the elasticity of

amenities with respect to population size.

We repeat the exercise in Figure 5 but now we let ζ = 0.02 as well. Figure 6 shows the

results. The results are qualitatively similar but now we observe that more cities become

extremely small. That is, the selection mechanism we emphasized above becomes stronger.

Equalizing city characteristics implies that externalities are not exploited as much. This

effect is bigger because of the two types of externalities. This explains why utility decreases

relative to Figure 5 for the counterfactuals on both effi ciency and excessive frictions. The

opposite result for amenities reflects that some of the larger cities have worse amenities, so

that eliminating amenity differences leads to a positive, though small, increase in utility.21

Perhaps surprisingly, the effects on utility of eliminating the differences in any of our three

characteristics are small in magnitude, even though the implied reallocation of agents is,

again, fairly large. Eliminating effi ciency differences increases utility by 0.8% but implies

that 41% of agents reallocate. The same reallocation statistics when we eliminate amenity

differences is 31% and 49% for excessive frictions. Most of the reallocation comes from the

extensive margin. Many cities become extremely small: the city selection effect. Once again,

by equalizing a given characteristic, some small cities lose their only comparative advantage.

This loss is compounded by the existence of externalities, so that some smaller cities become

so small that they exit. However, the reallocation has small effects on agents’utility, since

21Undoubtedly, there is a lot more uncertainty about the value of ζ than about the value of ω. In fact, it isnot entirely clear that city size leads to larger amenities. Hence, for robustness purposes, we have computedan alternative exercise where we let ζ = −0.02 instead of 0.02 (the rest of the parameters are kept exactly asin Figure 6). Comparing the results with those in Figure 6 indicates that the welfare gains from eliminatingheterogeneity in any one of the city characteristics are of similar magnitude (1.05% for effi ciency, 0.17% foramenities, and 0.93% for excessive frictions). The main change is that the city selection effect is now muchsmaller. This is natural since the negative externality of size on amenities favors small cities.

31

even though small cities do not experience the benefits of large externalities, they are not

distorted through taxes since city infrastructure is cheap. The slope of the envelope of the

value of living in different cities is extremely flat, so agents switching locations leads to small

utility gains.

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

Model Utility = 10

ActualModeled

8 10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)ln

(pro

b >

popu

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8 10 12 14 16 18-6

-5

-4

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ln(population)

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8 10 12 14 16 18-6

-5

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ln(p

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tion)



Figure 6: Counterfactuals Without Differences in One City Characteristic and

Externalities, κ = 0.001, ω = 0.02, ζ = 0.02

City selection can be most easily understood by studying what happens if we eliminate

differences in all three city characteristics. In this case the urban structure has 117 cities

with 1,752,525 agents and the other 75 cities essentially disappear and preserve a population

of only 538 agents in each of them. Without any city characteristics, but with externalities,

there are two city sizes that give agents identical utility levels, and the number of cities in

each size is determined by the market clearing condition so that all agents are housed in some

city. So there is an equilibrium that specifies the number of cities of each type. The utility

32

level in this case is 9.991. Thus, eliminating all differences in city characteristics yields small

losses to agents as most agents live in smaller cities and some live in very small towns that

have no congestion or infrastructure costs but also no gains from agglomeration. Note again

that since there are no shocks, we know that there may be multiple equilibria. As before, in

all cases we compute the equilibrium with minimal reallocation of agents across cities, which

yields a level of utility closest to the one in the actual distribution, namely, 10.

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

Figure 7: Counterfactuals Without Differences in City Characteristics, κ = 0.002

Figure 7 shows counterfactuals eliminating differences in all city characteristics for differ-

ent elasticities of city effi ciency and amenities to population size. Clearly, as we increase the

elasticity, and therefore the externality, we still have two sizes of cities, but the larger the

externality, the larger and fewer the larger cities. So larger externalities make the larger and

smaller cities larger and increase the number of small cities. Furthermore, the larger the

externality, the lower the utility in the counterfactual without differences in city character-

istics. When externalities are large, differences across cities create agglomeration and result

in benefits. Eliminating them yields lower utility.

33

5. CHINA

The most important finding so far is that eliminating differences in effi ciency, amenities

or excessive frictions leads to large reallocations of people but to small welfare effects. It is

unclear whether this conclusion is general, inherent to the model, or specific to the U.S. To

address this question, we carry out a similar analysis for the case of China.

The details of the database we built for 212 Chinese cities for 2005 are given in Online

Appendix B.2. The data we need are the same as for the U.S. and come from China City

Statistics and from the 2005 1% Population Survey. Two further comments are in order.

First, in China a prefecture-level city is an administrative division below a province and

above a county. Prefecture-level cities cover the entire Chinese geography. They include

both the urban parts and the rural hinterlands and are therefore not the same as cities in

the U.S. Luckily, the data tend to provide separate information for the urban parts of cities

(referred to as districts under prefecture-level cities or also as city proper). In our database

we focus on those districts under prefecture-level cities, as these are the closest equivalents

to MSAs in the U.S. Second, when using Chinese data, the issue of their quality inevitably

comes up. City-level data tend to be collected by local statistical agencies and are commonly

perceived to be of very high quality.22

In order to estimate Chinese city characteristics we need to use parameter values specific

to the Chinese economy. We set the capital share of income θ = 0.5221 and the real interest

rate r = 0.2008 (Bai et al., 2006). Consistent with our analysis of the U.S., we use the same

approach as McGrattan and Prescott (2010) to estimate ψ for China and find a value of

1.5247. We use a value of κ = 0.001, which we find using the same methodology as in the

U.S. case. Online Appendix B.2 provides more details. In any case, the exact values for

the different parameters play a limited role. When using the U.S. parameter values for our

exercise on China, the main findings are largely unchanged. The reason is that modifying

any of the parameter values has a limited impact on the distribution of the relevant variables

across cities. We set externalities equal to zero in all exercises with Chinese data.

For the purpose of comparison, we run the same benchmark counterfactual exercise as

22See Au and Henderson (2006) for a further discussion of the quality of city-level data in China.

34

in the case of the U.S. This exercise equalizes in turn each of the three city characteristics

(effi ciency, amenities and excessive frictions). Results for China are shown in Figure 8 and

should be compared to the results for the U.S. in Figure 2.23 The most striking difference

with the U.S. is that the welfare effects in China are now an order of magnitude larger. If all

Chinese cities had the same level of effi ciency, welfare would increase by 47%, and if all had

the same level of amenities, welfare would increase by 13%. The corresponding figures for

the U.S. are 1.2% and 0.2%.24 Another way of understanding the difference in magnitude is

that in order to maintain utility at its original level, it would be enough to give all Chinese

cities an effi ciency level corresponding to the lowest 27th percentile.

Note also that the total reallocation of population is similar to that in the U.S. even

though the welfare gains are much larger. Some examples can be informative: both Beijing

and Shanghai would lose about 97% of their population if we equalize productivity. In

contrast, if we equalize amenities, Beijing would lose 10% of its population, while Shanghai

would lose only 1%. Finally, when equalizing excessive frictions, the loss in population in

Beijing and Shanghai would be 29%.

When equalizing effi ciency or amenities across Chinese cities, the size distribution becomes

more dispersed, with the larger cities being larger and the smaller cities being smaller. In

contrast, in the U.S. the larger cities become smaller if we shut down effi ciency differences,

whereas the effect is less clear when we turn off amenity differences. Large cities in China

are in general more effi cient, but quite a few have worse amenities than smaller cities. If all

cities had the same amenities, some of the larger ones would become more attractive, making

them even larger. Given that larger cities tend to be more effi cient, it is not immediately

obvious why equalizing effi ciency levels skews the distribution toward larger cities. What

happens here is that some of the intermediate-sized cities, with higher amenities than the

largest cities, now get higher levels of effi ciency and end up becoming very large cities.

In other words, when equalizing amenities, the already larger cities become even larger,

23There is one difference with the exercise we perform for the U.S. When eliminating differences in a citycharacteristic, we set it equal to the median, rather than the weighted mean, of all cities. This changeunderestimates the difference between China and the U.S. We do this differently because the weighted meanof Chinese city TFP would make cities so productive that an equilibrium with the same number of citiesdoes not exist.24City characteristics in China were set equal to their median. Given that the median is below the mean,

the figures for China should be interpreted as lower bounds.

35

whereas when equalizing effi ciency, some intermediate-sized cities become much larger. This

is consistent with population reallocation being lower when equalizing amenities (50%) than

when equalizing effi ciency (64%).

12 13 14 15 16 17-6

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-4

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Model Utility = 10

ActualModeled

8 10 12 14 16 18-6

-5

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8 10 12 14 16 18-6

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12 13 14 15 16 17-6

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ln(p

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Figure 8: China Counterfactuals Without Differences in One City Characteristic

Another potential explanation is that large cities, even though they are better at every-

thing, are kept artificially small by migration restrictions. The relatively small population

combined with large effi ciency would lead our model to estimate low amenities for these

cities, leading to the mechanism described above. Shenzhen, one of the special economic

zone cities, is a case in point: its population would more than quadruple if we equalize

amenities. This would be in line with the finding of Au and Henderson (2006) that Chinese

cities are too small. This interpretation is also consistent with the much larger welfare effects

we find in China compared to the United States. If migratory restrictions are keeping highly

effi cient cities in China from reaching their optimal size, then equalizing amenities would

36

have an equivalent effect as lowering migratory barriers to these cities. As this leads to a

more effi cient allocation of factors of production, the welfare effect could be substantial.

We have not yet discussed the effect of equalizing excessive frictions across cities. When

setting excessive frictions equal to the median, we find that welfare declines by 1.5%. The

relatively small effect does not imply that excessive frictions are small in China. To see

this, Figure 9 shows the impact on welfare and the city size distribution of setting excessive

frictions to the 90th and the 10th percentile of the distribution of excessive frictions, a similar

exercise to the one we presented for the U.S. in Figure 4. If all cities had the excessive

frictions of the 90th percentile, welfare would drop by 5.8%, and the larger cities would

become smaller. Likewise, if all cities had the excessive frictions of the 10th percentile,

welfare would increase by 3.5%, and the larger cities would become larger. Overall, the

figure indicates that the changes in the size distribution of cities are smaller than in the

U.S., but the utility implications are similar in magnitude. In China, excessive frictions are

less important in explaining the dispersion in the size distribution of cities, but their average

level is as high as in the U.S.

12.5 13 13.5 14 14.5 15 15.5 16 16.5-6

-5

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ln(population)

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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

Figure 9: Changing Excessive Frictions in China

37

6. CONCLUSION

In this paper we have decomposed the size distribution of cities into three main characteris-

tics: effi ciency, amenities, and excessive frictions. We find that each one of these components

is important. Eliminating differences in any of them would imply large reallocations of peo-

ple. In the U.S. the welfare gains or losses associated with particular distributions of these

characteristics are modest. Eliminating any differences in characteristics across cities yields

welfare gains of at most 2%. Note that the actual population movements required can be

larger than 40%, so any small reallocation cost would turn these gains into losses. We also

include externalities in both productivity and amenities. The welfare effects associated with

eliminating particular characteristics of cities are even smaller in these cases, although we

find a strong selection effect in the counterfactual distributions. Namely, many cities exit or

become extremely small.

The small effects in terms of welfare are not inherent to the model. Applying the same

methodology to China reveals welfare effects that are an order of magnitude higher. Of

course, the impact on welfare could be further enhanced if one were to add distributional

effects in a model with heterogeneous agents. Also, if the number of cities were smaller,

reallocating by moving to similar cities becomes more diffi cult, implying larger welfare effects.

The results suggest that regional policies aimed at reducing spatial differences are likely

to have a small effect in the United States. In China, however, the impact could be much

larger. As argued before, this may be related to the high population mobility in the U.S.,

and the lack thereof in China.

More generally, we have provided a simple methodology to study the determinants of

the size distribution of cities. This methodology can be useful in comparing urban systems

across countries. We have illustrated this by also analyzing the case of China. The data

requirements to do the exercise are not extreme, and it could shed light on the sources of

differences in urban systems across countries. Such a comparison will be informative about

the effectiveness and welfare effects of different policies aimed at making the location of

agents across cities more effi cient.

The framework we presented could of course be extended to include additional features.

The demand for housing could be explicitly modeled and we might want to allow for hetero-

38

geneity in skills or preferences. Indeed, larger cities may differ from smaller cities in their

skill composition, in particular its dispersion if not its mean,25 and an agent’s preference for

living in nice weather might depend on his age. This would surely affect some of our results,

since heterogeneity might lead to less mobility across cities than assumed in the present

framework. But there is a tradeoff to be faced. Including such features would undoubtedly

make the model more realistic, but it would also increase the data requirements, thus limiting

the scope for comparing urban systems across countries.

REFERENCES

[1] Albouy, David. 2008. “Are Big Cities Really Bad Places to Live? Improving Quality-of-LifeEstimates across Cities.”NBER Working Paper 14472.

[2] Au, Chun-Chung, and J. Vernon Henderson. 2006. “Are Chinese Cities Too Small?”Review of Economic Studies, 73(3): 549-576.

[3] Bai, Chong-En, Chang-Tai Hsieh, and Yingyi Qian. 2006. “The Return to Capital inChina.”Brookings Papers on Economic Activity, 37(2): 61-102.

[4] Behrens, Kristian, Gilles Duranton, and Frédéric Robert-Nicoud. 2010. “Produc-tive Cities: Sorting, Selection, and Agglomeration.”CEPR Discussion Paper 7922.

[5] Behrens, Kristian, Giordano Mion, Yasusada Murata, and Jens Südekum. 2011.“Spatial Frictions.”CEP Discussion Paper 1108.

[6] Bleakley, Hoyt, and Jeffrey Lin. 2012. “Portage and Path Dependence.”Quarterly Jour-nal of Economics, 127(2): 587-644.

[7] Carlino, Gerald A., Satyajit Chatterjee, and Robert M. Hunt. 2007. “Urban Densityand the Rate of Invention.”Journal of Urban Economics, 61(3): 389-419.

[8] Chari, V. V., Patrick J. Kehoe, and Ellen R. McGrattan. 2007. “Business CycleAccounting.”Econometrica, 75(3): 781-836.

[9] Chatterjee, Satyajit, and Gerald A. Carlino. 2001. “Aggregate Metropolitan Em-ployment Growth and the Deconcentration of Metropolitan Employment.”Journal ofMonetary Economics, 48(3): 549-583.

[10] Combes, Pierre-Philippe, Gilles Duranton, Laurent Gobillon, Diego Puga, andSébastien Roux. 2012. “The Productivity Advantages of Large Cities: DistinguishingAgglomeration from Firm Selection.”Econometrica, forthcoming.

[11] Córdoba, Juan Carlos. 2008. “On the Distribution of City Sizes.”Journal of Urban Eco-nomics, 63(1): 177-197.

25Eeckhout, et al. (2011) presents evidence that the skill distribution has a similar mean, but fatter tails,in large versus small cities.

39

[12] Davis, Steven J., John C. Haltiwanger. 1992. “Gross Job Creation, Gross Job Destruc-tion, and Employment Reallocation.”Quarterly Journal of Economics, 107(3): 819-863.

[13] Davis, Donald R., and David E. Weinstein. 2002. “Bones, Bombs, and Break Points:The Geography of Economic Activity.”American Economic Review, 92(5): 1269-1289.

[14] Duranton, Gilles. 2007. “Urban Evolutions: The Fast, the Slow, and the Still.”AmericanEconomic Review, 97(1): 197-221.

[15] Duranton, Gilles, Henry G. Overman. 2008. “Exploring the Detailed Location Patternsof U.K. Manufacturing Industries Using Micro-Geographic Data.”Journal of RegionalScience, 48(1), 213-243.

[16] Eeckhout, Jan, Roberto Pinheiro, and Kurt Schmidheiny. 2011. “Spatial Sorting.”Unpublished.

[17] Gabaix, Xavier. 1999a. “Zipf’s Law for Cities: An Explanation.”Quarterly Journal ofEconomics, 114(3): 739-767.

[18] Gabaix, Xavier. 1999b. “Zipf’s Law and the Growth of Cities.”American Economic Re-view, 89(2): 129-132.

[19] Glaeser, Edward L., Jed Kolko, and Albert Saiz. 2001. “Consumer City.”Journal ofEconomic Geography, 1(1): 27-50.

[20] Glaeser, Edward L., Joseph Gyourko, and Raven Saks. 2005. “Why Is Manhattan SoExpensive? Regulation and the Rise in Housing Prices.”Journal of Law and Economics,48(2): 331-369.

[21] Holmes, Thomas J. 2005. “The Location of Sales Offi ces and the Attraction of Cities.”Journal of Political Economy, 113(3): 551-581.

[22] Holmes, Thomas J., and John J. Stevens. 2002. “Geographic Concentration and Es-tablishment Scale.”Review of Economics and Statistics, 84(4): 682-690.

[23] Lucas, Robert E. 1987. Models of Business Cycles. Oxford: Basil Blackwell.

[24] McGrattan, Ellen R., and Edward C. Prescott. 2010. “Unmeasured Investment andthe Puzzling U.S. Boom in the 1990s.”American Economic Journal: Macroeconomics,2(4): 88-123.

[25] Rappaport, Jordan. 2007. “Moving to Nice Weather.”Regional Science and Urban Eco-nomics, 37(3): 375-398.

[26] Rappaport, Jordan. 2008. “Consumption Amenities and City Population Density.”Re-gional Science and Urban Economics, 38(6): 533-552.

[27] Rappaport, Jordan. 2009. “The Increasing Importance of Quality of Life.” Journal ofEconomic Geography, 9(6): 779-804.

[28] Rappaport, Jordan, and Jeffrey D. Sachs. 2003. “The United States as a CoastalNation.”Journal of Economic Growth, 8(1): 5-46.

40

[29] Redding, Stephen J., and Daniel M. Sturm. 2008. “The Costs of Remoteness: Evidencefrom German Division and Reunification.”American Economic Review, 98(5): 1766-97.

[30] Roback, Jennifer. 1982. “Wages, Rents, and the Quality of Life.” Journal of PoliticalEconomy, 90(6): 1257-1278.

[31] Rosen, Sherwin. 1979. “Wage-based Indexes of Urban Quality of Life.”In Current Issuesin Urban Economics, ed. Peter Miezkowski and Mahlen Straszheim, 74-104. Baltimore:Johns Hopkins University Press.

[32] Rossi-Hansberg, Esteban, and Mark L. J. Wright. 2007. “Urban Structure andGrowth.”Review of Economic Studies, 74(2): 597-624.

[33] Storesletten, Kjetil, Chris I. Telmer, and and Amir Yaron. 2001. “The Welfare Costof Business Cycles Revisited: Finite Lives and Cyclical Variation in Idiosyncratic Risk.”European Economic Review, 45(7): 1311-1339.

41

APPENDIX A: CITY CHARACTERISTICS AND ROBUSTNESS (FORONLINE PUBLICATION)

‐30%

0%

30%

60%

90%

120%

150%

180%

210%

240%Columbia

Dayton

Tampa‐St. Petersburg‐Clearwater

Lubbock

Albuquerque

Oklah

oma City

Akron

Springfield

Nap

aTo

ledo

Orlan

do‐Kissimmee

Grand Rap

ids‐Wyoming

La Crosse

Syracuse

Detroit‐W

arren‐Livonia

Salem

San Francisco‐Oakland‐Fremont

Norw

ich‐New

London

Peo

ria

Baltimore‐Towson

Tulsa

Austin‐Round Rock

Eau Claire

Cincinnati‐Middletown

Den

ver‐Aurora‐Broomfield

Atlan

ta‐San

dy Springs‐M

arietta

Fort W

ayne

Los Angeles‐Long Beach‐San

ta Ana

Raleigh

‐Cary

Alban

y‐Schen

ectady‐Troy

Rochester

Boise City‐Nam

pa

Portland‐Van

couver‐Beaverton

Amarillo

Chicago‐Nap

erville‐Joliet

Jacksonville

Richmond

Las Vegas‐Parad

ise

Chattanooga

Cleveland‐Elyria‐Men

tor

Pittsburgh

Med

ford

Wichita

Harrisburg‐Carlisle

Boulder

Birmingham

‐Hoover

Mem

phis

Beaumont‐Port Arthur

Green

Bay

Waterloo‐Ced

ar Falls

Evan

sville

Billings

Kan

sas City

Portland‐South Portland‐Biddeford

Huntsville

Omah

a‐Council Bluffs

Ren

o‐Sparks

Milw

aukee‐Wau

kesha‐West Allis

Bloomington‐Norm

alDaven

port‐M

oline‐Rock Island

Dallas‐Fort W

orth‐Arlington

Charleston

Houston‐Sugar Lan

d‐Baytown

Columbus

Minneapolis‐St. Pau

l‐Bloomington

Baton Rouge

Philadelphia‐Cam

den

‐Wilm

ington

Appleton

Indianap

olis‐Carmel

Knoxville

Wau

sau

Lexington‐Fayette

New

York‐Northern New

Jersey‐Long Island

Roan

oke

Boston‐Cam

bridge‐Quincy

Ced

ar Rap

ids

Gulfport‐Biloxi

Santa Rosa‐Petaluma

Tren

ton‐Ewing

Durham

‐Chapel Hill

Hartford‐W

est H

artford‐East H

artford

Ban

gor

Sioux Falls

Winston‐Salem

Green

sboro‐High Point

San Antonio

Burlington‐South Burlington

Mad

ison

San Jo

se‐Sunnyvale ‐Santa Clara

Lafayette

San Luis Obispo‐Paso Robles

Des M

oines‐W

est Des M

oines

South Ben

d‐M

ishaw

aka

Charlotte‐Gastonia‐Concord

Fargo

Bridgeport‐Stamford‐Norw

alk

Percentage

Change in Population

Cities with Largest Percentage Change in City Population Without Amenity Differences

‐20%

0%

ion

Cities with Smallest Percentage Change in City Population Without Amenity Differences

‐30%

0%

30%

60%

90%

120%

150%

180%

210%

240%Columbia

Dayton


Lubbock

Albuquerque

Oklah

oma City

Akron

Springfield

Nap

aTo

ledo

Orlan

do‐Kissimmee

Grand Rap

ids‐Wyoming

La Crosse

Syracuse

Detroit‐W

arren‐Livonia

Salem


Norw

ich‐New

London

Peo

ria

Baltimore‐Towson

Tulsa

Austin‐Round Rock

Eau Claire


Den

ver‐Aurora‐Broomfield

Atlan

ta‐San

dy Springs‐M

arietta

Fort W

ayne

Los Angeles‐Long Beach‐San

ta Ana

Raleigh

‐Cary

Alban

y‐Schen

ectady‐Troy

Rochester

Boise City‐Nam

pa

Portland‐Van

couver‐Beaverton

Amarillo

Chicago‐Nap

erville‐Joliet

Jacksonville

Richmond

Las Vegas‐Parad

ise

Chattanooga


tor

Pittsburgh

Med

ford

Wichita


Boulder

Birmingham

‐Hoover

Mem

phis


Green

Bay

Waterloo‐Ced

ar Falls

Evan

sville

Billings

Kan

sas City


Huntsville

Omah

a‐Council Bluffs

Ren

o‐Sparks

Milw

aukee‐Wau

kesha‐West Allis

Bloomington‐Norm

alDaven

port‐M

oline‐Rock Island

Dallas‐Fort W

orth‐Arlington

Charleston

Houston‐Sugar Lan

d‐Baytown

Columbus


l‐Bloomington

Baton Rouge

Philadelphia‐Cam

den

‐Wilm

ington

Appleton

Indianap

olis‐Carmel

Knoxville

Wau

sau

Lexington‐Fayette

New

York‐Northern New

Jersey‐Long Island

Roan

oke

Boston‐Cam

bridge‐Quincy

Ced

ar Rap

ids

Gulfport‐Biloxi


Tren

ton‐Ewing

Durham

‐Chapel Hill

Hartford‐W

est H

artford‐East H

artford

Ban

gor

Sioux Falls

Winston‐Salem

Green

sboro‐High Point

San Antonio


Mad

ison

San Jo

se‐Sunnyvale ‐Santa Clara

Lafayette


Des M

oines‐W

est Des M

oines

South Ben

d‐M

ishaw

aka


Fargo


alk

Percentage



‐100%

‐80%

‐60%

‐40%

‐20%

0%

Poughkeep

sie‐New

burgh‐…

Modesto

Pueb

loDeltona‐Daytona Beach‐…

Brownsville‐Harlingen

Riverside‐San Bernardino‐ …

Stockton

Visalia‐Porterville

Johnstown

Coeu

r d'Alene

Laredo

Salinas

Hagerstown‐M

artinsburg

Ogden

‐Clearfield

Provo

‐Orem

Chico

Muskegon‐Norton Shores

Ocala

Punta Gorda

Pen

sacola‐Ferry Pass‐Brent

Cham

paign

‐Urbana

Holland‐Grand Haven

El Paso

Greeley

Tucson

Bloomington

Flint

Anderson

Palm Bay‐M

elbourne‐…

Fort Collins‐Loveland

Fresno

Bakersfield

Springfield

Santa Fe

Tallahassee

Santa Cruz‐Watsonville

Asheville

Jackson

Worcester

Utica‐Rome

Hickory‐Len

oir‐M

organ

ton

Yakima

Colorado Springs

Gainesville

Niles‐Ben

ton Harbor

Eugene‐Springfield

Augusta‐Richmond County

Kalam

azoo‐Portage

Bingham

ton

Bremerton‐Silverdale

York‐Han

over

Allentown‐Bethlehem

‐ …Fayetteville‐Springdale‐…

Jacksonville

McAllen‐Edinburg‐M

ission

Racine

Vinelan

d‐M

illville‐Bridgeton

Oxnard‐Thousand Oaks‐…

Topeka

Tuscaloosa

Lansing‐East Lan

sing

Savannah

Fayetteville

Can

ton‐M

assillon

Cap

e Coral‐Fort M

yers

Lynchburg

Johnson City

Rockford

Corpus Christi

Duluth

Bellingham

Columbus

Erie

Janesville

Scranton‐W

ilkes‐Barre

Virginia Beach‐Norfolk‐…

Reading

Mobile

Saginaw

‐Saginaw

…Sacram

ento‐Arden

‐Arcade‐…

Joplin

Youngstown‐W

arren‐ …

Salt Lake City

San Diego

‐Carlsbad

‐San

…Iowa City

Nap

les‐Marco Island

Phoen

ix‐M

esa‐Scottsdale

Buffalo‐Niagara Falls

Honolulu

Seattle‐Tacoma‐Bellevue

Spokane

Lancaster

Springfield

St. Louis

Huntington‐Ashland

Ann Arbor

Percentage



Figure A1: Changes in Population Sizes with Average Amenities

42

‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Columbia

Youngstown‐W

arren‐Boardman


Iowa City

San Diego

‐Carlsbad

‐San

Marcos

Salt Lake City

Billings


Sacram

ento‐Arden

‐Arcade‐Roseville

Amarillo

Scranton‐W

ilkes‐Barre

Johnson City

Lansing‐East Lan

sing

Erie

Racine

Boise City‐Nam

pa

Duluth

Corpus Christi

Chattanooga

Lubbock

Mobile

Rockford

Janesville


Tuscaloosa


Nap

les‐Marco Island

Niles‐Ben

ton Harbor

Lancaster

Lynchburg

La Crosse

Bingham

ton

Phoen

ix‐M

esa ‐Scottsdale

Ban

gor

Yakima

Topeka

Kalam

azoo‐Portage

York‐Han

over

Fayetteville‐Springdale‐Rogers


‐Easton

Anderson

Springfield

Colorado Springs

Utica‐Rome

Jackson

Vinelan

d‐M


Bakersfield

Gainesville

Eau Claire

El Paso

Fresno


Hickory‐Len

oir‐M

organ

ton

Can

ton‐M

assillon

Bloomington

Oxnard‐Thousand Oaks‐Ven

tura


Joplin

Tucson

Savannah

Worcester

Flint

Cham

paign

‐Urbana

Springfield

Tallahassee

Cap

e Coral‐Fort M

yers

St. Louis


Reading


Palm Bay‐M

elbourne‐Titusville

Pen


Bellingham

Med

ford

Chico


Asheville

Salinas

Stockton

Laredo


Ogden

‐Clearfield

Johnstown

Deltona‐Daytona Beach‐Orm

ond Beach

Pueb

loRiverside‐San Bernardino‐Ontario

Santa Fe

Modesto

Provo

‐Orem

Greeley

Punta Gorda

Poughkeep

sie‐New

burgh‐M

iddletown

Ocala


Coeu

r d'Alene

Hagerstown‐M

artinsburg


ission

Percentage


Cities with Largest Percentage Change in City Population Without Efficiency Differences

0%

20%

n

Cities with Smallest Percentage Change in City Population Without Efficiency Differences

‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Columbia

Youngstown‐W

arren‐Boardman


Iowa City

San Diego

‐Carlsbad

‐San

Marcos

Salt Lake City

Billings


Sacram

ento‐Arden


Amarillo

Scranton‐W

ilkes‐Barre

Johnson City

Lansing‐East Lan

sing

Erie

Racine

Boise City‐Nam

pa

Duluth

Corpus Christi

Chattanooga

Lubbock

Mobile

Rockford

Janesville


Tuscaloosa


Nap

les‐Marco Island

Niles‐Ben

ton Harbor

Lancaster

Lynchburg

La Crosse

Bingham

ton

Phoen

ix‐M

esa ‐Scottsdale

Ban

gor

Yakima

Topeka

Kalam

azoo‐Portage

York‐Han

over



‐Easton

Anderson

Springfield

Colorado Springs

Utica‐Rome

Jackson

Vinelan

d‐M


Bakersfield

Gainesville

Eau Claire

El Paso

Fresno


Hickory‐Len

oir‐M

organ

ton

Can

ton‐M

assillon

Bloomington


tura


Joplin

Tucson

Savannah

Worcester

Flint

Cham

paign

‐Urbana

Springfield

Tallahassee

Cap

e Coral‐Fort M

yers

St. Louis


Reading


Palm Bay‐M


Pen


Bellingham

Med

ford

Chico


Asheville

Salinas

Stockton

Laredo


Ogden

‐Clearfield

Johnstown

Deltona‐Daytona Beach‐Orm

ond Beach

Pueb

loRiverside‐San Bernardino‐Ontario

Santa Fe

Modesto

Provo

‐Orem

Greeley

Punta Gorda

Poughkeep

sie‐New

burgh‐M

iddletown

Ocala


Coeu

r d'Alene

Hagerstown‐M

artinsburg


ission

Percentage



‐100%

‐80%

‐60%

‐40%

‐20%

0%

20%

Bridgeport‐Stamford‐…

Charlotte‐Gastonia‐…

Lafayette

San Luis Obispo‐Paso …

Durham

‐Chapel Hill

Des M

oines‐W

est Des …

San …

Hartford‐W

est …

Tren

ton‐Ewing

New

York‐Northern …

Houston‐Sugar …

Boston‐Cam

bridge‐Qu…

Baton Rouge

Sioux Falls

Green

sboro‐High Point

Philadelphia‐Cam

den

‐…Charleston

Winston‐Salem

Indianap

olis‐Carmel

Gulfport‐Biloxi

Milw

aukee‐…

Evan

sville


l‐…

Dallas‐Fort W

orth‐…

Daven

port‐M

oline‐…

Mad

ison

South Ben

d‐M

ishaw

aka


tor


Knoxville

Pittsburgh

Mem

phis

Bloomington‐Norm

alOmah

a‐Council Bluffs

Green

Bay

Boulder

Lexington‐Fayette

Birmingham

‐Hoover


Chicago‐Nap

erville‐…

Columbus

San Antonio

Kan

sas City

Waterloo‐Ced

ar Falls

Richmond

Wichita


Ced

ar Rap

ids

Detroit‐W

arren‐Livonia

Rochester


Fort W

ayne

Huntsville

Portland‐Van

couver‐…

Fargo

Los Angeles‐Long …

Peo

ria

Las Vegas‐Parad

ise

Ren

o‐Sparks

Dayton

Den

ver‐Aurora‐…

Syracuse

Burlington‐South …

Ann Arbor

Tulsa

San Francisco‐…

Toledo

Appleton

Alban

y‐Schen

ectady‐…

Salem

Atlan

ta‐San

dy Springs‐…

Baltimore‐Towson

Austin‐Round Rock

Nap

aBuffalo‐Niagara Falls

Oklah

oma City


Columbus

Springfield

Norw

ich‐New

London

Wau

sau

Jacksonville

Honolulu

Raleigh

‐Cary

Spokane

Grand Rap

ids‐Wyoming

Orlan

do‐Kissimmee

Jacksonville

Virginia Beach‐…

Albuquerque

Akron

Portland‐South …

Fayetteville

Saginaw

‐Saginaw

…Roan

oke

Percentage



Figure A2: Changes in Population Sizes with Average Effi ciency

43

1100%

1300%

1500%ulation

Cities with Largest Percentage Change in City Population Without Excessive Friction Differences

100%

300%

500%

700%

900%

1100%

1300%

1500%Percentage

Chan

ge in

Population


‐100%

100%

300%

500%

700%

900%

1100%

1300%

1500%

Colorado Springs


alk


Pensacola‐Ferry Pass‐Brent

Ren

o‐Sparks

Des Moines‐W

est Des Moines

Toledo

Wichita

Tallahassee

Dayton

Lexington‐Fayette



Youngstown‐W

arren‐Boardman

Mobile

El Paso

Naples‐Marco Island

Winston‐Salem

Syracuse

Salinas



Eau Claire

Hickory‐Len

oir‐M

organton

York‐Hanover

Baton Rouge



Flint

Huntsville


Amarillo

Joplin


South Ben

d‐M

ishaw

aka

Greeley

Lubbock

Corpus Christi

Salt Lake City

Appleton

Rockford

Ced

ar Rapids

Punta Gorda


Laredo

Lansing‐East Lansing

Billings

Johnstown

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Gainesville

Davenport‐M

oline‐Rock Island

Erie

Chico


Peoria

Pueblo

Lynchburg

Norw

ich‐New London

Duluth

Spokane

La Crosse

Trenton‐Ewing

Wausau

Topeka

Green

Bay

Boulder

Ann Arbor



Durham

‐Chapel Hill

Vineland‐M


Bingham

ton

Gulfport‐Biloxi

Cham

paign

‐Urbana

Evansville

Janesville

Tuscaloosa



Fayetteville

Charleston

Yakima

Lafayette

ginaw

‐Saginaw

Township North

Jackson

Johnson City

Springfield

Bloomington

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

alIowa City

Columbus

Niles‐Ben

ton Harbor

Napa

Anderson

Jacksonville

Percentage

Chan

ge in

Population


‐100%

100%

300%

500%

700%

900%

1100%

1300%

1500%

Colorado Springs


alk



Ren

o‐Sparks

Des Moines‐W

est Des Moines

Toledo

Wichita

Tallahassee

Dayton

Lexington‐Fayette



Youngstown‐W

arren‐Boardman

Mobile

El Paso


Winston‐Salem

Syracuse

Salinas



Eau Claire

Hickory‐Len

oir‐M

organton

York‐Hanover

Baton Rouge



Flint

Huntsville


Amarillo

Joplin


South Ben

d‐M

ishaw

aka

Greeley

Lubbock

Corpus Christi

Salt Lake City

Appleton

Rockford

Ced

ar Rapids

Punta Gorda


Laredo


Billings

Johnstown

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Gainesville

Davenport‐M

oline‐Rock Island

Erie

Chico


Peoria

Pueblo

Lynchburg

Norw

ich‐New London

Duluth

Spokane

La Crosse

Trenton‐Ewing

Wausau

Topeka

Green

Bay

Boulder

Ann Arbor



Durham

‐Chapel Hill

Vineland‐M


Bingham

ton

Gulfport‐Biloxi

Cham

paign

‐Urbana

Evansville

Janesville

Tuscaloosa



Fayetteville

Charleston

Yakima

Lafayette

Saginaw

‐Saginaw

Township North

Jackson

Johnson City

Springfield

Bloomington

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

alIowa City

Columbus

Niles‐Ben

ton Harbor

Napa

Anderson

Jacksonville

Percentage

Chan

ge in

Population


60%

80%

Cities with Smallest Percentage Change in City Population Without Excessive Friction Differences

‐100%

100%

300%

500%

700%

900%

1100%

1300%

1500%

Colorado Springs


alk



Ren

o‐Sparks

Des Moines‐W

est Des Moines

Toledo

Wichita

Tallahassee

Dayton

Lexington‐Fayette



Youngstown‐W

arren‐Boardman

Mobile

El Paso


Winston‐Salem

Syracuse

Salinas



Eau Claire

Hickory‐Len

oir‐M

organton

York‐Hanover

Baton Rouge



Flint

Huntsville


Amarillo

Joplin


South Ben

d‐M

ishaw

aka

Greeley

Lubbock

Corpus Christi

Salt Lake City

Appleton

Rockford

Ced

ar Rapids

Punta Gorda


Laredo


Billings

Johnstown

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Gainesville

Davenport‐M

oline‐Rock Island

Erie

Chico


Peoria

Pueblo

Lynchburg

Norw

ich‐New London

Duluth

Spokane

La Crosse

Trenton‐Ewing

Wausau

Topeka

Green

Bay

Boulder

Ann Arbor



Durham

‐Chapel Hill

Vineland‐M


Bingham

ton

Gulfport‐Biloxi

Cham

paign

‐Urbana

Evansville

Janesville

Tuscaloosa



Fayetteville

Charleston

Yakima

Lafayette

Saginaw

‐Saginaw

Township North

Jackson

Johnson City

Springfield

Bloomington

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

alIowa City

Columbus

Niles‐Ben

ton Harbor

Napa

Anderson

Jacksonville

Percentage

Chan

ge in

Population


‐40%

‐20%

0%

20%

40%

60%

80%

ntage Chan

ge in

Population


‐100%

100%

300%

500%

700%

900%

1100%

1300%

1500%

Colorado Springs


alk



Ren

o‐Sparks

Des Moines‐W

est Des Moines

Toledo

Wichita

Tallahassee

Dayton

Lexington‐Fayette



Youngstown‐W

arren‐Boardman

Mobile

El Paso


Winston‐Salem

Syracuse

Salinas



Eau Claire

Hickory‐Len

oir‐M

organton

York‐Hanover

Baton Rouge



Flint

Huntsville


Amarillo

Joplin


South Ben

d‐M

ishaw

aka

Greeley

Lubbock

Corpus Christi

Salt Lake City

Appleton

Rockford

Ced

ar Rapids

Punta Gorda


Laredo


Billings

Johnstown

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Gainesville

Davenport‐M

oline‐Rock Island

Erie

Chico


Peoria

Pueblo

Lynchburg

Norw

ich‐New London

Duluth

Spokane

La Crosse

Trenton‐Ewing

Wausau

Topeka

Green

Bay

Boulder

Ann Arbor



Durham

‐Chapel Hill

Vineland‐M


Bingham

ton

Gulfport‐Biloxi

Cham

paign

‐Urbana

Evansville

Janesville

Tuscaloosa



Fayetteville

Charleston

Yakima

Lafayette

Saginaw

‐Saginaw

Township North

Jackson

Johnson City

Springfield

Bloomington

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

alIowa City

Columbus

Niles‐Ben

ton Harbor

Napa

Anderson

Jacksonville

Percentage

Chan

ge in

Population


‐100%

‐80%

‐60%

‐40%

‐20%

0%

20%

40%

60%

80%

ork‐Northern New …

geles‐Long Beach‐…

e‐San Bernardino‐…

x‐Mesa‐Scottsdale

o‐Naperville‐Joliet

nta‐Sandy Springs‐…

t Worth‐Arlington

elphia‐Cam

den

‐Wil …

e‐Sunnyvale‐Santa …

Tampa‐St. …

Sioux Falls

Cam

bridge‐Quincy

it‐W

arren‐Livonia

uston‐Sugar Land‐…

nneapolis‐St. Paul‐…

rancisco‐Oakland‐…

Baltimore‐Towson

Salem

eepsie‐Newburgh‐…

town‐M

artinsburg

rlando‐Kissimmee

‐Edinburg‐M

ission

Aurora‐Broomfield

acramen

to‐Arden

‐…Kansas City

San Antonio

Columbus

iego

‐Carlsbad

‐San

…rtland‐Vancouver‐…

as Vegas‐Paradise

Jacksonville

Pittsburgh

nnati‐Middletown

St. Louis

Austin‐Round Rock

d‐Thousand Oaks‐…

e Coral‐Fort M

yers

on‐Norton Shores

Reading

Santa Fe

Medford

Luis Obispo‐Paso …

Modesto

dianapolis‐Carmel

and‐Elyria‐Mentor

Raleigh

‐Cary

nia Beach‐Norfolk‐…

Worcester

Springfield

Boise City‐Nam

pa

Chattanooga

Ocala

Provo

‐Orem

Coeu

r d'Alene

harlotte‐Gastonia‐…

Memphis

Oklahoma City

d‐South Portland‐…

Asheville

town‐Bethlehem

‐ …aukee‐Waukesha‐…

Tucson

Savannah

rmingham

‐Hoover

Richmond

Springfield

Stockton

Ogden

‐Clearfield

Schen

ectady‐Troy

m Bay‐M

elbourne‐…

rd‐W

est Hartford‐…

Albuquerque

Lancaster

Rapids‐Wyoming

Fresno

ffalo‐Niagara Falls

Madison

Rochester

Akron

Columbia

Fargo

Tulsa

a‐Daytona Beach‐ …

Roanoke

Canton‐M

assillon

aha‐Council Bluffs

Honolulu

Knoxville

Bangor

Bellingham

nsboro‐High Point

Bakersfield

Percentage

Chan

ge in

Population


‐100%

100%

300%

500%

700%

900%

1100%

1300%

1500%

Colorado Springs


alk



Ren

o‐Sparks

Des Moines‐W

est Des Moines

Toledo

Wichita

Tallahassee

Dayton

Lexington‐Fayette



Youngstown‐W

arren‐Boardman

Mobile

El Paso


Winston‐Salem

Syracuse

Salinas



Eau Claire

Hickory‐Len

oir‐M

organton

York‐Hanover

Baton Rouge



Flint

Huntsville


Amarillo

Joplin


South Ben

d‐M

ishaw

aka

Greeley

Lubbock

Corpus Christi

Salt Lake City

Appleton

Rockford

Ced

ar Rapids

Punta Gorda


Laredo


Billings

Johnstown

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Gainesville

Davenport‐M

oline‐Rock Island

Erie

Chico


Peoria

Pueblo

Lynchburg

Norw

ich‐New London

Duluth

Spokane

La Crosse

Trenton‐Ewing

Wausau

Topeka

Green

Bay

Boulder

Ann Arbor



Durham

‐Chapel Hill

Vineland‐M


Bingham

ton

Gulfport‐Biloxi

Cham

paign

‐Urbana

Evansville

Janesville

Tuscaloosa



Fayetteville

Charleston

Yakima

Lafayette

Saginaw

‐Saginaw

Township North

Jackson

Johnson City

Springfield

Bloomington

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

alIowa City

Columbus

Niles‐Ben

ton Harbor

Napa

Anderson

Jacksonville

Percentage

Chan

ge in

Population


‐100%

‐80%

‐60%

‐40%

‐20%

0%

20%

40%

60%

80%

New York‐Northern New …

Los Angeles‐Long Beach‐…

Riverside‐San

Bernardino‐…

Phoenix‐M

esa‐Scottsdale

Chicago‐Naperville‐Joliet

Atlanta‐Sandy Springs‐ …

Dallas‐Fort W

orth‐Arlington

Philadelphia‐Cam

den

‐Wil …

San Jose‐Sunnyvale‐Santa …

Tampa‐St. …

Sioux Falls

Boston‐Cam

bridge‐Quincy

Detroit‐W

arren‐Livonia

Houston‐Sugar Land‐ …

Minneapolis‐St. Paul‐…

San Francisco‐Oakland‐…

Baltimore‐Towson

Salem

Poughkeepsie‐Newburgh‐ …

Hagerstown‐M

artinsburg

Orlando‐Kissimmee


ission

Denver‐Aurora‐Broomfield

Sacram

ento‐Arden

‐ …Kansas City

San Antonio

Columbus

San Diego

‐Carlsbad

‐San

…Portland‐Vancouver‐…

Las Vegas‐Paradise

Jacksonville

Pittsburgh


St. Louis

Austin‐Round Rock


Cape Coral‐Fort M

yers


Reading

Santa Fe

Medford


Modesto

Indianapolis‐Carmel

Cleveland‐Elyria‐Mentor

Raleigh

‐Cary

Virginia Beach‐Norfolk‐ …

Worcester

Springfield

Boise City‐Nam

pa

Chattanooga

Ocala

Provo

‐Orem

Coeu

r d'Alene

Charlotte‐Gastonia‐ …

Memphis

Oklahoma City

Portland‐South Portland‐ …

Asheville


‐ …Milw

aukee‐W

aukesha‐…

Tucson

Savannah

Birmingham

‐Hoover

Richmond

Springfield

Stockton

Ogden

‐Clearfield

Albany‐Schenectady‐Troy

Palm Bay‐M

elbourne‐ …

Hartford‐W

est Hartford‐…

Albuquerque

Lancaster

Grand Rapids‐Wyoming

Fresno


Madison

Rochester

Akron

Columbia

Fargo

Tulsa

Deltona‐Daytona Beach‐ …

Roanoke

Canton‐M

assillon

Omaha‐Council Bluffs

Honolulu

Knoxville

Bangor

Bellingham

Green

sboro‐High Point

Bakersfield

Percentage

Chan

ge in

Population


Figure A3: Changes in Population Sizes with Average Excessive Frictions

44

150%

180%

210%

240%Population


‐30%

0%

30%

60%

90%

120%

150%

180%

210%

240%

a k r n e y d n a e o g e e m a t n a e n a k n d a e a y y r a n o t e d e a r h d a e r r s r y e s s y e d s sl s d n n n s n e n l n e d e u y e s xi a g l d s m t r o n n a e s s a d o k

Percentage

Chan

ge in

Population


‐30%

0%

30%

60%

90%

120%

150%

180%

210%

240%

Columbia

Lubbock


Dayton

Albuquerque

Oklahoma City

Springfield

Akron

Napa

Orlando‐Kissimmee

Toledo


La Crosse

Syracuse

Salem

Detroit‐W

arren‐Livonia


Norw

ich‐New London

Peoria

Eau Claire

Baltimore‐Towson

Tulsa

Austin‐Round Rock



Atlanta‐Sandy Springs‐M

arietta

Fort W

ayne

Los Angeles‐Long Beach‐Santa Ana

Raleigh

‐Cary


Rochester

Boise City‐Nam

pa

Portland‐Vancouver‐Beaverton

Amarillo


Jacksonville

Richmond


Chattanooga


Pittsburgh

Medford

Wichita


Boulder

Birmingham

‐Hoover

Memphis


Green

Bay

Evansville

Waterloo‐Ced

ar Falls

Billings

Kansas City

Huntsville



Milw

aukee‐W

aukesha‐West Allis

Bloomington‐Norm

alRen

o‐Sparks

Davenport‐M

oline‐Rock Island

Charleston

Dallas‐Fort W

orth‐Arlington

Houston‐Sugar Land‐Baytown

Columbus

Minneapolis‐St. Paul‐Bloomington

Baton Rouge

Philadelphia‐Cam

den

‐Wilm

ington


Appleton

Knoxville

ew York‐Northern New Jersey‐Long Island

Lexington‐Fayette

Wausau

Boston‐Cam

bridge‐Quincy

Roanoke

Ced

ar Rapids

Gulfport‐Biloxi


Trenton‐Ewing

Durham

‐Chapel Hill

Hartford‐W

est Hartford‐East Hartford

Sioux Falls

Winston‐Salem

Green

sboro‐High Point

Bangor

San Antonio


Madison

San Jose‐Sunnyvale‐Santa Clara

Lafayette


Des Moines‐W

est Des Moines

South Ben

d‐M

ishaw

aka


Fargo


alk

Percentage

Chan

ge in

Population


‐30%

0%

30%

60%

90%

120%

150%

180%

210%

240%

Columbia

Lubbock


Dayton

Albuquerque

Oklahoma City

Springfield

Akron

Napa

Orlando‐Kissimmee

Toledo


La Crosse

Syracuse

Salem

Detroit‐W

arren‐Livonia


Norw

ich‐New London

Peoria

Eau Claire

Baltimore‐Towson

Tulsa

Austin‐Round Rock




arietta

Fort W

ayne


Raleigh

‐Cary


Rochester

Boise City‐Nam

pa


Amarillo


Jacksonville

Richmond


Chattanooga


Pittsburgh

Medford

Wichita


Boulder

Birmingham

‐Hoover

Memphis


Green

Bay

Evansville

Waterloo‐Ced

ar Falls

Billings

Kansas City

Huntsville



Milw

aukee‐W


Bloomington‐Norm

alRen

o‐Sparks

Davenport‐M

oline‐Rock Island

Charleston

Dallas‐Fort W

orth‐Arlington


Columbus


Baton Rouge

Philadelphia‐Cam

den

‐Wilm

ington


Appleton

Knoxville

New York‐Northern New Jersey‐Long Island

Lexington‐Fayette

Wausau

Boston‐Cam

bridge‐Quincy

Roanoke

Ced

ar Rapids

Gulfport‐Biloxi


Trenton‐Ewing

Durham

‐Chapel Hill

Hartford‐W


Sioux Falls

Winston‐Salem

Green

sboro‐High Point

Bangor

San Antonio


Madison


Lafayette


Des Moines‐W

est Des Moines

South Ben

d‐M

ishaw

aka


Fargo


alk

Percentage

Chan

ge in

Population


0%


‐30%

0%

30%

60%

90%

120%

150%

180%

210%

240%

Columbia

Lubbock


Dayton

Albuquerque

Oklahoma City

Springfield

Akron

Napa

Orlando‐Kissimmee

Toledo


La Crosse

Syracuse

Salem

Detroit‐W

arren‐Livonia


Norw

ich‐New London

Peoria

Eau Claire

Baltimore‐Towson

Tulsa

Austin‐Round Rock




arietta

Fort W

ayne


Raleigh

‐Cary


Rochester

Boise City‐Nam

pa


Amarillo


Jacksonville

Richmond


Chattanooga


Pittsburgh

Medford

Wichita


Boulder

Birmingham

‐Hoover

Memphis


Green

Bay

Evansville

Waterloo‐Ced

ar Falls

Billings

Kansas City

Huntsville



Milw

aukee‐W


Bloomington‐Norm

alRen

o‐Sparks

Davenport‐M

oline‐Rock Island

Charleston

Dallas‐Fort W

orth‐Arlington


Columbus


Baton Rouge

Philadelphia‐Cam

den

‐Wilm

ington


Appleton

Knoxville


Lexington‐Fayette

Wausau

Boston‐Cam

bridge‐Quincy

Roanoke

Ced

ar Rapids

Gulfport‐Biloxi


Trenton‐Ewing

Durham

‐Chapel Hill

Hartford‐W


Sioux Falls

Winston‐Salem

Green

sboro‐High Point

Bangor

San Antonio


Madison


Lafayette


Des Moines‐W

est Des Moines

South Ben

d‐M

ishaw

aka


Fargo


alk

Percentage

Chan

ge in

Population


‐60%

‐40%

‐20%

0%

ntage Chan

ge in

Population


‐30%

0%

30%

60%

90%

120%

150%

180%

210%

240%

Columbia

Lubbock


Dayton

Albuquerque

Oklahoma City

Springfield

Akron

Napa

Orlando‐Kissimmee

Toledo


La Crosse

Syracuse

Salem

Detroit‐W

arren‐Livonia


Norw

ich‐New London

Peoria

Eau Claire

Baltimore‐Towson

Tulsa

Austin‐Round Rock




arietta

Fort W

ayne


Raleigh

‐Cary


Rochester

Boise City‐Nam

pa


Amarillo


Jacksonville

Richmond


Chattanooga


Pittsburgh

Medford

Wichita


Boulder

Birmingham

‐Hoover

Memphis


Green

Bay

Evansville

Waterloo‐Ced

ar Falls

Billings

Kansas City

Huntsville



Milw

aukee‐W


Bloomington‐Norm

alRen

o‐Sparks

Davenport‐M

oline‐Rock Island

Charleston

Dallas‐Fort W

orth‐Arlington


Columbus


Baton Rouge

Philadelphia‐Cam

den

‐Wilm

ington


Appleton

Knoxville


Lexington‐Fayette

Wausau

Boston‐Cam

bridge‐Quincy

Roanoke

Ced

ar Rapids

Gulfport‐Biloxi


Trenton‐Ewing

Durham

‐Chapel Hill

Hartford‐W


Sioux Falls

Winston‐Salem

Green

sboro‐High Point

Bangor

San Antonio


Madison


Lafayette


Des Moines‐W

est Des Moines

South Ben

d‐M

ishaw

aka


Fargo


alk

Percentage

Chan

ge in

Population


‐100%

‐80%

‐60%

‐40%

‐20%

0%

Johnstown

gon‐Norton Shores

a Cruz‐Watsonville

Springfield


Colorado Springs

Utica‐Rome


Gainesville

Jackson

Savannah

‐Len

oir‐M

organton

e Coral‐Fort M

yers

Anderson

Bakersfield

Fresno

Bellingham

Worcester

Tallahassee

lland‐Grand Haven

Cham

paign

‐Urbana

m Bay‐M

elbourne‐…

El Paso

Bloomington

Asheville

Santa Fe

la‐Ferry Pass‐Brent

Chico

Tucson

Flint

ort Collins‐Loveland

Salinas

Ogden

‐Clearfield

Laredo

Stockton

stown‐M

artinsburg

ownsville‐Harlingen

Coeu

r d'Alene

Pueblo

na‐Daytona Beach‐…

Modesto

keep

sie‐Newburgh‐…

de‐San Bernardino‐…

Provo

‐Orem

Punta Gorda

Ocala

Greeley

Yakima

iles‐Ben

ton Harbor

Kalam

azoo‐Portage

‐Richmond County

Bingham

ton

emerton‐Silverdale

York‐Hanover

ntown‐Bethlehem

‐…tteville‐Springdale‐…

rd‐Thousand Oaks‐…

‐Millville‐Bridgeton

Racine

Topeka

Jacksonville

Tuscaloosa

Canton‐M

assillon

ansing‐East Lansing

Fayetteville

Lynchburg

Rockford

Johnson City

Corpus Christi

Duluth

n‐Edinburg‐M

ission

Columbus

Reading

Erie

Janesville

Joplin

anton‐W

ilkes‐Barre

Mobile


Sacram

ento‐Arden

‐…Saginaw

‐Saginaw

…ungstown‐W

arren‐…

Salt Lake City

Diego

‐Carlsbad

‐San

…Iowa City

aples‐Marco Island

ix‐M

esa‐Scottsdale

St. Louis

uffalo‐Niagara Falls

Honolulu

Lancaster

e‐Tacoma‐Bellevue

Spokane

Springfield

untington‐Ashland

Ann Arbor

Percentage

Chan

ge in

Population


‐30%

0%

30%

60%

90%

120%

150%

180%

210%

240%

Columbia

Lubbock


Dayton

Albuquerque

Oklahoma City

Springfield

Akron

Napa

Orlando‐Kissimmee

Toledo


La Crosse

Syracuse

Salem

Detroit‐W

arren‐Livonia


Norw

ich‐New London

Peoria

Eau Claire

Baltimore‐Towson

Tulsa

Austin‐Round Rock




arietta

Fort W

ayne


Raleigh

‐Cary


Rochester

Boise City‐Nam

pa


Amarillo


Jacksonville

Richmond


Chattanooga


Pittsburgh

Medford

Wichita


Boulder

Birmingham

‐Hoover

Memphis


Green

Bay

Evansville

Waterloo‐Ced

ar Falls

Billings

Kansas City

Huntsville



Milw

aukee‐W


Bloomington‐Norm

alRen

o‐Sparks

Davenport‐M

oline‐Rock Island

Charleston

Dallas‐Fort W

orth‐Arlington


Columbus


Baton Rouge

Philadelphia‐Cam

den

‐Wilm

ington


Appleton

Knoxville


Lexington‐Fayette

Wausau

Boston‐Cam

bridge‐Quincy

Roanoke

Ced

ar Rapids

Gulfport‐Biloxi


Trenton‐Ewing

Durham

‐Chapel Hill

Hartford‐W


Sioux Falls

Winston‐Salem

Green

sboro‐High Point

Bangor

San Antonio


Madison


Lafayette


Des Moines‐W

est Des Moines

South Ben

d‐M

ishaw

aka


Fargo


alk

Percentage

Chan

ge in

Population


‐100%

‐80%

‐60%

‐40%

‐20%

0%

Johnstown



Springfield


Colorado Springs

Utica‐Rome


Gainesville

Jackson

Savannah

Hickory‐Len

oir‐M

organton

Cape Coral‐Fort M

yers

Anderson

Bakersfield

Fresno

Bellingham

Worcester

Tallahassee


Cham

paign

‐Urbana

Palm Bay‐M

elbourne‐…

El Paso

Bloomington

Asheville

Santa Fe


Chico

Tucson

Flint


Salinas

Ogden

‐Clearfield

Laredo

Stockton

Hagerstown‐M

artinsburg


Coeu

r d'Alene

Pueblo

Deltona‐Daytona Beach‐…

Modesto

Poughkeepsie‐Newburgh‐…

Riverside‐San

Bernardino‐…

Provo

‐Orem

Punta Gorda

Ocala

Greeley

Yakima

Niles‐Ben

ton Harbor

Kalam

azoo‐Portage


Bingham

ton


York‐Hanover


‐…Fayetteville‐Springdale‐…


Vineland‐M


Racine

Topeka

Jacksonville

Tuscaloosa

Canton‐M

assillon


Fayetteville

Lynchburg

Rockford

Johnson City

Corpus Christi

Duluth


ission

Columbus

Reading

Erie

Janesville

Joplin

Scranton‐W

ilkes‐Barre

Mobile

Virginia Beach‐Norfolk‐…

Sacram

ento‐Arden

‐…Saginaw

‐Saginaw

…Yo

ungstown‐W

arren‐…

Salt Lake City

San Diego

‐Carlsbad

‐San

…Iowa City


Phoenix‐M

esa‐Scottsdale

St. Louis


Honolulu

Lancaster


Spokane

Springfield


Ann Arbor

Percentage

Chan

ge in

Population


Figure A4: Changes in Population Sizes with Average Amenities (with Externalities)

45

‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Amarillo

Orlan

do‐Kissimmee

Youngstown‐W

arren‐Boardman


Columbia

Salt Lake City

Virginia Beach‐Norfolk‐New

port New

sJohnson City

Scranton‐W

ilkes‐Barre

Ban

gor

Erie

Racine

Duluth

La Crosse

Lubbock

Janesville

San Diego

‐Carlsbad

‐San

Marcos

Lansing‐East Lan

sing

Chattanooga

Boise City‐Nam

pa

Corpus Christi

Sacram

ento‐Arden


Mobile

Tuscaloosa


Rockford


Niles‐Ben

ton Harbor

Nap

les‐Marco Island

Lynchburg

Bingham

ton

Lancaster

Topeka

Yakima


Kalam

azoo‐Portage

Eau Claire

York‐Han

over

Anderson

Vinelan

d‐M



Jackson

Springfield

Utica‐Rome

Gainesville


‐Easton

Colorado Springs

Phoen

ix‐M

esa‐Scottsdale


Bakersfield

Joplin

Bloomington

Hickory‐Len

oir‐M

organ

ton

El Paso

Can

ton‐M

assillon

Fresno


Cham

paign

‐Urbana

Savannah


tura

Flint

Worcester

Tallahassee

Tucson

Springfield

St. Louis


Cap

e Coral‐Fort M

yers


Reading

Med

ford

Bellingham

Palm Bay‐M


Chico

Pen


Asheville


Salinas

Laredo


Stockton

Ogden

‐Clearfield

Johnstown

Pueb

loDeltona‐Daytona Beach‐Orm

ond Beach

Santa Fe

Modesto

Riverside‐San Bernardino‐Ontario

Punta Gorda

Provo

‐Orem

Greeley

Poughkeep

sie‐New

burgh‐M

iddletown

Ocala


Coeu

r d'Alene

Hagerstown‐M

artinsburg


ission

Percentage



0%

20%

on


‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Amarillo

Orlan

do‐Kissimmee

Youngstown‐W

arren‐Boardman


Columbia

Salt Lake City

Virginia Beach‐Norfolk‐New

port New

sJohnson City

Scranton‐W

ilkes‐Barre

Ban

gor

Erie

Racine

Duluth

La Crosse

Lubbock

Janesville

San Diego

‐Carlsbad

‐San

Marcos

Lansing‐East Lan

sing

Chattanooga

Boise City‐Nam

pa

Corpus Christi

Sacram

ento‐Arden


Mobile

Tuscaloosa


Rockford


Niles‐Ben

ton Harbor

Nap

les‐Marco Island

Lynchburg

Bingham

ton

Lancaster

Topeka

Yakima


Kalam

azoo‐Portage

Eau Claire

York‐Han

over

Anderson

Vinelan

d‐M



Jackson

Springfield

Utica‐Rome

Gainesville


‐Easton

Colorado Springs

Phoen

ix‐M

esa‐Scottsdale


Bakersfield

Joplin

Bloomington

Hickory‐Len

oir‐M

organ

ton

El Paso

Can

ton‐M

assillon

Fresno


Cham

paign

‐Urbana

Savannah


tura

Flint

Worcester

Tallahassee

Tucson

Springfield

St. Louis


Cap

e Coral‐Fort M

yers


Reading

Med

ford

Bellingham

Palm Bay‐M


Chico

Pen


Asheville


Salinas

Laredo


Stockton

Ogden

‐Clearfield

Johnstown

Pueb

loDeltona‐Daytona Beach‐Orm

ond Beach

Santa Fe

Modesto

Riverside‐San Bernardino‐Ontario

Punta Gorda

Provo

‐Orem

Greeley

Poughkeep

sie‐New

burgh‐M

iddletown

Ocala


Coeu

r d'Alene

Hagerstown‐M

artinsburg


ission

Percentage



‐100%

‐80%

‐60%

‐40%

‐20%

0%

20%

Bridgeport‐Stamford‐…

Lafayette

Gulfport‐Biloxi

Hartford‐W

est …

San Jo

se‐Sunnyvale‐…

Green

sboro‐High Point

Mad

ison

Winston‐Salem

Tren

ton‐Ewing

Durham

‐Chapel Hill

South Ben

d‐M

ishaw

aka


Fargo

Des M

oines‐W

est Des …

Charlotte‐Gastonia‐…

Charleston

Baton Rouge

Evan

sville

Houston‐Sugar Lan

d‐…

Sioux Falls

Boston‐Cam

bridge‐…

Daven

port‐M

oline‐…

Indianap

olis‐Carmel


Milw

aukee‐Wau

kesha‐…

Bloomington‐Norm

alNew

York‐Northern …

Philadelphia‐Cam

den

‐…Beaumont‐Port Arthur

Green

Bay

Knoxville

Waterloo‐Ced

ar Falls

Boulder

Lexington‐Fayette


l‐…

Ced

ar Rap

ids


tor

Omah

a‐Council Bluffs

Mem

phis

Dallas‐Fort W

orth‐…

San Antonio

Birmingham

‐Hoover

Burlington‐South …

Pittsburgh


Wichita

Huntsville

Columbus

Fort W

ayne

Richmond

Kan

sas City

Appleton

Wau

sau

Ren

o‐Sparks

Rochester

Peo

ria

Nap

aChicago‐Nap

erville‐Joliet

Syracuse

Ann Arbor


Portland‐Van

couver‐…

Dayton

Detroit‐W

arren‐Livonia

Springfield

Tulsa

Norw

ich‐New

London

Las Vegas‐Parad

ise

Toledo


Alban

y‐Schen

ectady‐…

Den

ver‐Aurora‐…

Columbus

Spokane

Roan

oke

Austin‐Round Rock

San Francisco‐Oakland‐…

Billings


Oklah

oma City

Honolulu

Salem

Jacksonville


Baltimore‐Towson

Raleigh

‐Cary

Jacksonville

Portland‐South …

Saginaw

‐Saginaw

…Iowa City

Grand Rap

ids‐Wyoming

Fayetteville

Atlan

ta‐San

dy Springs‐…

Akron

Albuquerque

Percentage



Figure A5: Changes in Population Sizes with Average Effi ciency (with Externalities)

46

700%

800%

900%ulation


0%

100%

200%

300%

400%

500%

600%

700%

800%

900%Percentage

Chan

ge in

Population


‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Knoxville

Green

sboro‐High Point

Bakersfield

Bellingham

Bangor

Colorado Springs


alk



Des Moines‐W

est Des Moines

Ren

o‐Sparks

Toledo

Wichita

Dayton

Tallahassee

Lexington‐Fayette


Youngstown‐W

arren‐Boardman

El Paso

Mobile

Syracuse

Winston‐Salem




Salinas

Baton Rouge


Hickory‐Len

oir‐M

organton

York‐Hanover

Flint


Huntsville




Eau Claire

Amarillo

South Ben

d‐M

ishaw

aka

Joplin

Greeley

Lubbock

Corpus Christi

Salt Lake City

Rockford

Appleton


Ced

ar Rapids


Laredo

Punta Gorda

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Billings

Johnstown

Davenport‐M

oline‐Rock Island

Gainesville

Erie


Peoria

Chico

Norw

ich‐New London

Duluth

Spokane

Lynchburg

Trenton‐Ewing

Pueblo

Green

Bay

Topeka

La Crosse

Wausau

Boulder

Ann Arbor

Durham

‐Chapel Hill



Bingham

ton

Vineland‐M


Evansville

Gulfport‐Biloxi

Cham

paign

‐Urbana

Tuscaloosa


Fayetteville

Janesville

Charleston

Yakima


Lafayette

ginaw

‐Saginaw

Township North

Springfield

Johnson City

Jackson

Bloomington

Columbus

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

al

Percentage

Chan

ge in

Population


‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Knoxville

Green

sboro‐High Point

Bakersfield

Bellingham

Bangor

Colorado Springs


alk



Des Moines‐W

est Des Moines

Ren

o‐Sparks

Toledo

Wichita

Dayton

Tallahassee

Lexington‐Fayette


Youngstown‐W

arren‐Boardman

El Paso

Mobile

Syracuse

Winston‐Salem




Salinas

Baton Rouge


Hickory‐Len

oir‐M

organton

York‐Hanover

Flint


Huntsville




Eau Claire

Amarillo

South Ben

d‐M

ishaw

aka

Joplin

Greeley

Lubbock

Corpus Christi

Salt Lake City

Rockford

Appleton


Ced

ar Rapids


Laredo

Punta Gorda

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Billings

Johnstown

Davenport‐M

oline‐Rock Island

Gainesville

Erie


Peoria

Chico

Norw

ich‐New London

Duluth

Spokane

Lynchburg

Trenton‐Ewing

Pueblo

Green

Bay

Topeka

La Crosse

Wausau

Boulder

Ann Arbor

Durham

‐Chapel Hill



Bingham

ton

Vineland‐M


Evansville

Gulfport‐Biloxi

Cham

paign

‐Urbana

Tuscaloosa


Fayetteville

Janesville

Charleston

Yakima


Lafayette

Saginaw

‐Saginaw

Township North

Springfield

Johnson City

Jackson

Bloomington

Columbus

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

al

Percentage

Chan

ge in

Population


60%

80%


‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Knoxville

Green

sboro‐High Point

Bakersfield

Bellingham

Bangor

Colorado Springs


alk



Des Moines‐W

est Des Moines

Ren

o‐Sparks

Toledo

Wichita

Dayton

Tallahassee

Lexington‐Fayette


Youngstown‐W

arren‐Boardman

El Paso

Mobile

Syracuse

Winston‐Salem




Salinas

Baton Rouge


Hickory‐Len

oir‐M

organton

York‐Hanover

Flint


Huntsville




Eau Claire

Amarillo

South Ben

d‐M

ishaw

aka

Joplin

Greeley

Lubbock

Corpus Christi

Salt Lake City

Rockford

Appleton


Ced

ar Rapids


Laredo

Punta Gorda

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Billings

Johnstown

Davenport‐M

oline‐Rock Island

Gainesville

Erie


Peoria

Chico

Norw

ich‐New London

Duluth

Spokane

Lynchburg

Trenton‐Ewing

Pueblo

Green

Bay

Topeka

La Crosse

Wausau

Boulder

Ann Arbor

Durham

‐Chapel Hill



Bingham

ton

Vineland‐M


Evansville

Gulfport‐Biloxi

Cham

paign

‐Urbana

Tuscaloosa


Fayetteville

Janesville

Charleston

Yakima


Lafayette

Saginaw

‐Saginaw

Township North

Springfield

Johnson City

Jackson

Bloomington

Columbus

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

al

Percentage

Chan

ge in

Population


‐40%

‐20%

0%

20%

40%

60%

80%

ntage Chan

ge in

Population


‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Knoxville

Green

sboro‐High Point

Bakersfield

Bellingham

Bangor

Colorado Springs


alk



Des Moines‐W

est Des Moines

Ren

o‐Sparks

Toledo

Wichita

Dayton

Tallahassee

Lexington‐Fayette


Youngstown‐W

arren‐Boardman

El Paso

Mobile

Syracuse

Winston‐Salem




Salinas

Baton Rouge


Hickory‐Len

oir‐M

organton

York‐Hanover

Flint


Huntsville




Eau Claire

Amarillo

South Ben

d‐M

ishaw

aka

Joplin

Greeley

Lubbock

Corpus Christi

Salt Lake City

Rockford

Appleton


Ced

ar Rapids


Laredo

Punta Gorda

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Billings

Johnstown

Davenport‐M

oline‐Rock Island

Gainesville

Erie


Peoria

Chico

Norw

ich‐New London

Duluth

Spokane

Lynchburg

Trenton‐Ewing

Pueblo

Green

Bay

Topeka

La Crosse

Wausau

Boulder

Ann Arbor

Durham

‐Chapel Hill



Bingham

ton

Vineland‐M


Evansville

Gulfport‐Biloxi

Cham

paign

‐Urbana

Tuscaloosa


Fayetteville

Janesville

Charleston

Yakima


Lafayette

Saginaw

‐Saginaw

Township North

Springfield

Johnson City

Jackson

Bloomington

Columbus

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

al

Percentage

Chan

ge in

Population


‐100%

‐80%

‐60%

‐40%

‐20%

0%

20%

40%

60%

80%

Anderson

Jacksonville

es‐Ben

ton Harbor

Napa

Iowa City

town‐M

artinsburg

Angeles‐Long …

ork‐Northern New …

verside‐San …

x‐Mesa‐Scottsdale

o‐Naperville‐Joliet

nta‐Sandy Springs‐…

t Worth‐Arlington

adelphia‐Cam

den

‐…pa‐St. Petersburg‐…

e‐Sunnyvale‐Santa …

Sioux Falls

Cam

bridge‐Quincy

eepsie‐Newburgh‐…

it‐W

arren‐Livonia

uston‐Sugar Land‐…

nneapolis‐St. Paul‐…

Baltimore‐Towson

rancisco‐Oakland‐…

Salem

‐Edinburg‐M

ission

rlando‐Kissimmee

Aurora‐Broomfield

acramen

to‐Arden

‐…San Antonio

Kansas City

Columbus

iego

‐Carlsbad

‐San

…rtland‐Vancouver‐…

as Vegas‐Paradise

St. Louis

Jacksonville

Pittsburgh

on‐Norton Shores

nnati‐Middletown

Medford

Austin‐Round Rock

d‐Thousand Oaks‐…

e Coral‐Fort M

yers

Santa Fe

Reading

Modesto

Luis Obispo‐Paso …

dianapolis‐Carmel

Raleigh

‐Cary

and‐Elyria‐Mentor


Worcester

Springfield

Boise City‐Nam

pa

Chattanooga

Ocala

Coeu

r d'Alene

Provo

‐Orem

harlotte‐Gastonia‐…

Memphis

d‐South Portland‐…

Oklahoma City

Asheville

town‐Bethlehem

‐ …aukee‐Waukesha‐…

Tucson

Savannah

rmingham

‐Hoover

Springfield

Richmond

Stockton

Ogden

‐Clearfield

Schen

ectady‐Troy

m Bay‐M

elbourne‐…

rd‐W

est Hartford‐…

Albuquerque

Lancaster

Rapids‐Wyoming

Fresno

ffalo‐Niagara Falls

Madison

Rochester

Akron

Columbia

Tulsa

Fargo

a‐Daytona Beach‐ …

Roanoke

aha‐Council Bluffs

Canton‐M

assillon

Honolulu

Percentage

Chan

ge in

Population


‐100%

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

Knoxville

Green

sboro‐High Point

Bakersfield

Bellingham

Bangor

Colorado Springs


alk



Des Moines‐W

est Des Moines

Ren

o‐Sparks

Toledo

Wichita

Dayton

Tallahassee

Lexington‐Fayette


Youngstown‐W

arren‐Boardman

El Paso

Mobile

Syracuse

Winston‐Salem




Salinas

Baton Rouge


Hickory‐Len

oir‐M

organton

York‐Hanover

Flint


Huntsville




Eau Claire

Amarillo

South Ben

d‐M

ishaw

aka

Joplin

Greeley

Lubbock

Corpus Christi

Salt Lake City

Rockford

Appleton


Ced

ar Rapids


Laredo

Punta Gorda

Scranton‐W

ilkes‐Barre

Utica‐Rome

Kalam

azoo‐Portage

Fort W

ayne

Billings

Johnstown

Davenport‐M

oline‐Rock Island

Gainesville

Erie


Peoria

Chico

Norw

ich‐New London

Duluth

Spokane

Lynchburg

Trenton‐Ewing

Pueblo

Green

Bay

Topeka

La Crosse

Wausau

Boulder

Ann Arbor

Durham

‐Chapel Hill



Bingham

ton

Vineland‐M


Evansville

Gulfport‐Biloxi

Cham

paign

‐Urbana

Tuscaloosa


Fayetteville

Janesville

Charleston

Yakima


Lafayette

Saginaw

‐Saginaw

Township North

Springfield

Johnson City

Jackson

Bloomington

Columbus

Waterloo‐Ced

ar Falls

Racine

Bloomington‐Norm

al

Percentage

Chan

ge in

Population


‐100%

‐80%

‐60%

‐40%

‐20%

0%

20%

40%

60%

80%

Anderson

Jacksonville

Niles‐Ben

ton Harbor

Napa

Iowa City

Hagerstown‐M

artinsburg


New York‐Northern New …

Riverside‐San

…Phoenix‐M

esa‐Scottsdale


Atlanta‐Sandy Springs‐ …

Dallas‐Fort W

orth‐Arlington

Philadelphia‐Cam

den

‐ …Tampa‐St. Petersburg‐…

San Jose‐Sunnyvale‐Santa …

Sioux Falls

Boston‐Cam

bridge‐Quincy

Poughkeepsie‐Newburgh‐ …

Detroit‐W

arren‐Livonia

Houston‐Sugar Land‐ …

Minneapolis‐St. Paul‐…

Baltimore‐Towson

San Francisco‐Oakland‐ …

Salem


ission

Orlando‐Kissimmee


Sacram

ento‐Arden

‐ …San Antonio

Kansas City

Columbus

San Diego

‐Carlsbad

‐San

…Portland‐Vancouver‐…


St. Louis

Jacksonville

Pittsburgh



Medford

Austin‐Round Rock


Cape Coral‐Fort M

yers

Santa Fe

Reading

Modesto



Raleigh

‐Cary


Virginia Beach‐Norfolk‐ …

Worcester

Springfield

Boise City‐Nam

pa

Chattanooga

Ocala

Coeu

r d'Alene

Provo

‐Orem

Charlotte‐Gastonia‐ …

Memphis

Portland‐South Portland‐ …

Oklahoma City

Asheville


‐ …Milw

aukee‐W

aukesha‐…

Tucson

Savannah

Birmingham

‐Hoover

Springfield

Richmond

Stockton

Ogden

‐Clearfield


Palm Bay‐M

elbourne‐ …

Hartford‐W

est Hartford‐…

Albuquerque

Lancaster


Fresno


Madison

Rochester

Akron

Columbia

Tulsa

Fargo

Deltona‐Daytona Beach‐ …

Roanoke


Canton‐M

assillon

Honolulu

Percentage

Chan

ge in

Population


Figure A6: Changes in Population Sizes with Average Excessive Frictions (withExternalities)

47

Without Differences in Amenities: Without Differences in Efficiency:

Without Differences in Excessive Frictions:

Figure A7: Maps of Changes in Population Sizes

48

Without Differences in Amenities: Without Differences in Efficiency:

Without Differences in Excessive Frictions:

Figure A8: Maps of Changes in Population Sizes with Externalities, ω = 0.02

49

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

ActualModeled

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



6 8 10 12 14 16 18 20-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



0 5 10 15 20-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)



Figure A9: Elasticity of Commuting Costs with Respect to Population Equal to 0.25

50

11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

ActualModeled

10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

Average Efficiency

10 12 14 16 18-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

Average Amenities

9 10 11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> po

pula

tion)

Average Excessive Frictions

ActualAll Ages: U = 10.089, R = 0.44Age <= 70: U = 10.079, R = 0.44Age <= 65: U = 10.076, R = 0.44

ActualAll Ages: U = 10.122, R = 0.37Ages <= 70: U = 10.159, R = 0.45Ages <= 65: U = 10.174, R = 0.49

ActualAll Ages: U = 10.019, R = 0.20Ages <= 70: U = 10.023, R = 0.21Ages <= 65: U = 10.028, R = 22

Figure A10: Equalizing Differences in One City Characteristic with Age Cutoffs for HoursWorked

51

10 11 12 13 14 15 16 17-6

-5

-4

-3

-2

-1

0

ln(population)

ln(p

rob

> p

opul

atio

n)

Actual Distribution, Utility = 10Optimal Allocation, Utility = 10.0578

Figure A11: Optimal Allocation with Externalities, ω = 0.02

52

APPENDIX B: DATA APPENDIX (FOR ONLINE PUBLICATION)

B.1 United States

This section provides a detailed description of the U.S. metropolitan data we use.

Unit of observation. The unit of observation is the metropolitan statistical area (MSA).A metropolitan statistical area is a collection of counties with at least one urbanized areaof 50,000 or more inhabitants. We use data from 2005 to 2008. Going further back in timeis complex, since the definition of MSAs changed in 2003, and there was a subsequent lagin the adoption of the new definitions. More recent data (for 2009) are not available yet forsome of the relevant variables.

Production. Measured by Gross Domestic Product by Metropolitan Area. Source: Bu-reau of Economic Analysis, Regional Economic Accounts.

Population. Data on population come from the Bureau of Economic Analysis, RegionalEconomic Accounts.

Private consumption. The measure of consumption used to compute the labor wedgeis private consumption. There are no ready-to-use data on private consumption at themetropolitan area level. We start by decomposing private consumption into private con-sumption net of housing services and private consumption of housing services.We proxy private consumption net of housing services by retail earnings. In particular,

we use retail earnings (at the MSA level) multiplied by private consumption net of housing(at the U.S. level) divided by retail earnings (at the U.S. level). Data on retail earningsare defined as personal earnings from retail trade and come from the Bureau of EconomicAnalysis Regional Economic Accounts, Table CA05. Data on private consumption net ofhousing come from the Bureau of Economic Analysis National Income and Product Accounts(NIPA), Table 2.3.5. In using this proxy, we follow the literature on interregional risk sharing,which has used retail sales as a proxy for private consumption (Asdrubali et al., 1996, Hessand Shin, 1997, Lustig and Van Nieuwerburgh, 2010). Note that those papers use retailsales, rather than retail earnings, by using data from the Survey of Buying Power publishedby Sales & Marketing Management. However, that survey was interrupted during the period2006-2008. Both proxies are very similar, though. For 2005 and 2008 the correlation betweenretail earnings and retail sales at the MSA level is about 0.80. In addition, the correlationbetween private consumption and retail earnings at the U.S. level for the years 2001-2008 is0.99.We proxy private consumption of housing services by taking the sum of aggregate gross

rent of renter-occupied housing and the rental value of the aggregate value of owner-occupiedhousing. Both variables are available at the MSA level and come from the annual American

53

Community Survey run by the U.S. Census Bureau. To compute the rental value of owner-occupied housing, we assume that the aggregate value of owner-occupied housing is thediscounted sum of future rental flows, taking into account depreciation. The rental value ofowner-occupied housing is then computed as the aggregate value of owner-occupied housingmultiplied by r+δ and divided by 1+r. For the benchmark calculation, we take r = δ = 0.02,as in the rest of the paper.

Capital stock. Again, there are no ready-to-use capital stock data at the MSA level. Westart by decomposing the capital stock into non-residential and residential capital.We proxy non-residential capital at the MSA level by using sectoral non-residential capital

stock data at the U.S. level and allocating it to the different MSAs as a function of theirsectoral weights. This is similar to the approach taken by Garofalo and Yamarik (2002) whenestimating state capital stocks. Sectoral non-residential capital stock data come from theNational Economic Accounts from the BEA. We take the sum of private and public capital.For private non-residential capital we take current-cost net stock of private fixed assets byindustry (Table 3.1ES); for public non-residential capital we take current-cost net stock ofgovernment fixed assets at both the federal level and the state and local level (Table 7.1B).We then allocate the sectoral capital stock to the MSAs as a function of their shares ofsectoral earnings. In particular, capital stock in sector s in MSA i is computed as the capitalstock in sector s in the U.S. multiplied by earnings in sector s in MSA i divided by earningsin sector s in the U.S. Data on sectoral earnings both at the MSA and the U.S. levels comefrom the Regional Economic Accounts of the Bureau of Economic Analysis (Table CA05N).Residential capital at the MSA level is easier to come by. We take the sum of the aggregate

value of renter-occupied and owner-occupied housing. In the case of owner-occupied housing,that information is available from the American Community Survey of the U.S. CensusBureau. In the case of renter-occupied housing, the same data source gives information onthe aggregate gross rent. This allows us to compute the value of rental-occupied housing asthe aggregate gross rent multiplied by 1 + r divided by r + δ. This assumes, as before, thatthe value of housing is equal to the discounted sum of future rental streams, where futurerental streams are the same as today’s rental stream corrected for depreciation.

Hours worked. To compute average hours worked we take the total hours worked dividedby the population age 16 years old and above. We use data from the Current PopulationSurvey (CPS) and compute total hours worked at the MSA level by summing up the totalhours worked by individuals (weighted by their representativeness in the sample) and thendividing them by all individuals age 16 and above in the sample (weighted by their represen-tativeness in the sample). To limit errors due to small sample problems, we leave out MSAsthat have information on less than 50 individuals. The share of time worked is then equalto the average hours worked per day divided by 14.

Wages. Data on average wages per job come from the Bureau of Economic Analysis.

54

Housing rental prices. As a measure for housing rental prices, we take the median grossrent of rental-occupied housing. Data at the MSA level are available from the AmericanCommunity Survey from the U.S. Census Bureau.

Labor tax rate. We measure the labor tax rate as the federal and state income taxliability (after credits) divided by total income. Data come from the Current PopulationSurvey (CPS). As with the case of hours worked, we aggregate federal and state income taxliability across individuals at the MSA level and divide it by the sum of total income acrossthose same individuals. As before, individuals are weighted by their representativeness inthe CPS.

Consumption tax rate. We take the sum of (i) the sales tax revenue by all local gov-ernments within the MSA and (ii) the sales tax revenue by the state which we assign to thedifferent MSAs in function of their weights in the state’s retail income. Data on sales taxrevenue come from State & Local Government Finance, U.S. Census Bureau. This datasetgives detailed information on all types of revenue for all types of local and state governments.To compute the sales tax revenue by all local governments at the MSA level, note that

the data are available at the county level, which we then aggregate up to the MSA level. Weselect all revenue categories that correspond to sales tax revenue (T09, T10, T11, T12, T13,T14, T15, T16, and T19). One issue is that the dataset only has information on counties thatrespond, but not all do. For those counties that did not respond, the U.S. Census Bureauimputes values, but only makes those imputed values available at the state level, withoutproviding a breakdown at the county level. For counties with missing records, we impute thedata by taking the sales tax revenue at the local level in revenue category x (at the state level)multiplied by retail personal income (at the MSA level) divided by retail personal income(at the state level). Retail personal income comes from the Regional Economic Accounts ofthe BEA. Once we have sales revenue data (reported or imputed) in all categories at thecounty level, we aggregate them to the MSA level. For sales tax revenue by states, we assignit to the MSAs within states using their relative weights in retail personal earnings fromthe Regional Economic Accounts of the BEA. The consumption tax rate is then sales taxrevenue divided by private consumption.

Places. Population data of U.S. places come from the 2010 Census.

Amenities. To validate our estimates of amenities, we collect data on 23 observed ameni-ties at the MSA level. First, we use data on 8 climate variables from www.weatherbase.comtypically used in the literature on amenities: average low in January, annual days in ex-cess of 90 degrees, annual days below 32 degrees, annual precipitation, number of days withprecipitation, number of days with precipitation > 0.2 inch, relative humidity in July, andJuly heat index (average of relative humidity and high temperature). Second, we use thequality-of-life variables in Rappaport (2008). These come from the Places Rated Almanac

55

by Savageau (2000) and the Cities Ranked & Rated by Sperling and Sander (2004). Fromthe Places Rated Almanac we take 6 variables (transport, education, crime, arts, health,and recreation) and from the Cities Ranked & Rated we use 7 variables (education, health,crime, transport, leisure, arts & culture, and quality of life). All of the 13 variables from thePlaces Rated Almanac and Cities Ranked & Rated are constructed such that lower valuescorrespond to “better”amenities. Third, from Rappaport and Sachs (2003) we use 2 vari-ables on proximity to water: closeness (< 20 km) to a body of water (Ocean, Gulf, GreatLakes) and closeness (< 20 km) to a body of water or major river. In Table B.1 we reportthe correlations between our estimate of amenities and those 23 measures.

Government spending. We split up government spending into federal government spend-ing and state and local government spending. To estimate federal spending by MSA we takeearnings by federal civilian government and military at the MSA level, and multiply it bythe ratio of federal government spending in the state of the MSA to the earnings by federalcivilian government and military in the state of the MSA. This way of proceeding is reason-able, given that the correlation between federal spending and federal earnings at the statelevel ranges between 0.95 and 0.98. Federal civilian and military earnings come from theRegional Economic Accounts of the BEA. Federal government spending by state comes fromthe Consolidated Federal Funds Report of the U.S Census Bureau. It measures the sum ofprocurement contracts, salaries and wages, and grants, and thus leaves out transfers andloans. To estimate state and local government spending, we follow a similar procedure. Wetake state and local government wages at the MSA level, and multiply it by the ratio of stateand local government spending in the state of the MSA to the state and local governmentwages in the state of the MSA. Once again, the rationale is based on the high correlation atthe state level between state and local spending and state and local wages (0.99). State andlocal government wages come from the Regional Economic Accounts of the BEA. State andlocal government spending by state comes from the State and Local Government Financedata of the U.S. Census Bureau. It measures the sum of current operations and capitaloutlays, thus leaving out transfers and subsidies.

Other measures of excessive frictions. When validating our estimates of excessivefrictions, we use a number of additional variables. Time spent commuting comes from theAmerican Community of the U.S. Census Bureau. Data on unionization come from theUnion Membership and Coverage Database constructed by Hirsch and Macpherson, andis available online at www.unionstats.com. Finally, to measure land regulation, we use theWharton Residential Land Use Regulatory Index. For a description of the data, see Gyourko,Saiz and Summers (2008).

B.2 China

This section provides a detailed description of the Chinese city-level data we use.

56

Unit of observation. The unit of observation is Districts under Prefecture-Level Cities.This corresponds to the urban part of Prefecture-Level Cities, sometimes referred to as thecity proper. Note that Prefecture-Level Cities cover the entire Chinese geography and includeboth the urban parts (proxied for by Districts under Prefecture-Level Cities) and the ruralhinterlands. We focus on 2005 and have data on 212 cities.

Production. Measured by Gross Domestic Product at the level ofDistricts under Prefecture-Level Cities. Source: China City Statistics, China Data Center.

Private consumption. To compute private consumption at the level of Districts underPrefecture-Level Cities, we multiply retail sales of consumer goods at the level of Districtsunder Prefecture-Level Cities by the ratio of final consumption expenditure to total retailsales of consumer goods at the national level. Source: China City Statistics and NationalStatistics, China Data Center.

Population. Population and Population age 15 years and above. Source: China CityStatistics, China Data Center.

Hours worked. To compute average hours worked we take the total hours worked dividedby the population 15 years old and above. We use the 2005 1% Population Survey to getdata on the population age 15 years and above, population employed, and average hoursworked by the employed. We then multiply population employed by average hours workedby employed and divide it by the population age 15 years and above. These data are availablefor most Prefecture-Level Cities but often not for Districts under Prefecture-Level Cities. Inorder not to lose too many observations, we use the data at the level of Prefecture-LevelCities.

Parameter values. Bai et al. (2006) provide time series estimates for the capital shareof income and for the real interest rate. Taking the average for 2000-2005, we set θ = 0.5221

and r = 0.2008. To be consistent with the case of the U.S., where we took ψ from McGrattanand Prescott (2010), we use the same formula as they do: ψ = (1−τh)(1−θ)(1−h)

1+τc)ch, where c is

consumption per capita (data defined above), h are hours worked as share of total hours(average hours worked per year as defined above divided by 5110), τh is the tax rate onlabor (defined as personal income tax as a share of personal income) and τ c the tax rate onconsumption (defined as the sum of consumption tax and value added tax as a share of totalconsumption expenditures). The data needed to compute these tax rates come from theNational Bureau of Statistics of China and are for 2004. This gives us a value ψ = 1.5247.

57

Appendix References

Asdrubali, Pierfederico, Bent E. Sorensen, and Oved Yosha. 1996. “Channels ofInterstate Risk Sharing: United States 1963-1990.”Quarterly Journal of Economics, 111(4):1081-1110.

Garofalo, Gasper A., and Steven Yamarik. 2002. “Regional Convergence: Evidencefrom a New State-by-State Capital Stock Series.”Review of Economics and Statistics, 84(2):316-323.

Gyourko, Joseph, Albert Saiz, and Anita Summers. 2008. “A New Measure of theLocal Regulatory Environment for Housing Markets: The Wharton Residential Land UseRegulatory Index.”Urban Studies, 45(3): 693-729.

Hess, Gregory D., and Kwanho Shin. 1997. “International and Intranational BusinessCycles.”Oxford Review of Economic Policy, 13(3): 93-109.

Lustig, Hanno, and Stijn Van Nieuwerburgh. 2010. “How Much Does Household Col-lateral Constrain Regional Risk Sharing?”Review of Economic Dynamics, 13(2): 265-294.

Savageau, David. 2000. Places Rated Almanac, with Ralph d’Agostino. Foster City, CA:IDG Books Worldwide, Inc.

Sperling, Bert, and Peter Sander. 2004. Cities Ranked & Rated, First Edition. Hobo-ken, NJ: Wiley Publishing, Inc.

58

Table B.1: Correlation between Estimated Amenities and Standard Measures of Amenities

Correlation P-value Expected Sign

Weather

Average low in January 0.2306 0.0015 Yes

Annual days in excess of 90 degrees 0.2744 0.0001 No

Annual days below 32 -0.1628 0.0276 Yes

Annual precipitation -0.1581 0.0285 Yes

Number of days with precipitation -0.2523 0.0005 Yes

Number of days with precipitation > 0.2 inch -0.2640 0.0058 Yes

Relative humidity in July -0.2006 0.0103 Yes

July heat index -0.0942 0.2315 Yes

Places Rated Almanac

Transport -0.4950 0.0000 Yes

Education -0.4923 0.0000 Yes

Crime -0.0542 0.4616 Yes

Arts -0.4950 0.0000 Yes

Health -0.5252 0.0000 Yes

Recreation -0.3075 0.0000 Yes

Cities Ranked & Rated

Education -0.3996 0.0000 Yes

Health -0.1310 0.0739 Yes

Crime -0.0824 0.2625 Yes

Transport -0.3489 0.0000 Yes

Leisure -0.0377 0.6084 Yes

Arts & Culture -0.3879 0.0000 Yes

Quality of Life -0.2258 0.0019 Yes

Distance to Water

< 20 km to a body of water 0.0957 0.1867 Yes

< 20 km to a body of water or major river 0.1195 0.0988 Yes

59

Table B.2: Correlation between Effi ciency and Standard Measures of Productivity


Wages 0.7925 0.0000 Yes

Labor productivity 0.9003 0.0000 Yes

Table B.3: Correlation between Labor Wedges and Standard Measures of Frictions


Taxes

Labor tax rate 0.1915 0.0078 Yes

Consumption tax rate 0.2032 0.0047 Yes

Joint income & consumption tax* 0.2667 0.0002 Yes

Government spending

Federal spending per person 0.2589 0.0003 Yes

State & local spending per person 0.1472 0.0416 Yes

Total government spending per person 0.2821 0.0001 Yes

Commuting costs

Share of work time spent commuting 0.3947 0.0000 Yes

Unionization

Percentage unionization 0.1038 0.1702 Yes

Percentage unionization private sector 0.1523 0.0436 Yes

Percentage unionization public sector 0.0229 0.7633 Yes

Land regulation

Wharton index (WRLURI) -0.0728 0.3711 No

*This is the correlation between (1− τ) and (1− τh)/(1− τ c). All other correlations are with τ .

60

Table B.4: Data and Estimated City Characteristics

Data City Characteristics

Name Pop GDP Cons Cap Hours lnAi ln γi ln gi(’000s) (m$) (m$) (m$) (Annual)

Akron, OH 699 26777 19525 101675 1210 7.518 1.013 -0.112

Albany-Schenectady-Troy, NY 851 36605 25750 153250 1209 7.563 0.995 -0.176

Albuquerque, NM 823 33174 23325 138000 1215 7.519 1.019 -0.163

Allentown-Bethlehem-Easton, PA-NJ 797 27946 21375 131250 1188 7.400 1.070 -0.209

Amarillo, TX 241 8763 6776 30900 1260 7.492 0.990 0.220

Anderson, IN 131 3214 2313 13600 942 7.354 1.151 0.976

AnnArbor, MI 346 17743 9458 97525 1219 7.583 1.030 0.471

Appleton, WI 217 8953 6674 29525 1324 7.558 0.955 0.290

Asheville, NC 400 12730 11450 60025 1228 7.314 1.067 -0.149

Atlanta-SandySprings-Marietta, GA 5174 258875 153500 1160000 1361 7.562 0.998 -1.066

Augusta-RichmondCounty, GA-SC 525 16913 11800 71100 1114 7.425 1.090 0.164

Austin-RoundRock, TX 1559 73118 45450 322000 1292 7.561 1.004 -0.443

Bakersfield, CA 777 25476 17825 130500 1126 7.363 1.118 -0.045

Baltimore-Towson, MD 2659 125750 83800 630500 1215 7.562 1.005 -0.701

Bangor, ME 148 5062 5459 19775 1152 7.470 0.950 0.108

BatonRouge, LA 759 35904 19375 110450 1151 7.765 0.939 0.119

Beaumont-PortArthur, TX 377 13840 10121 42575 1021 7.675 0.965 0.372

Bellingham, WA 191 6958 6212 35925 1278 7.352 1.028 0.077

Billings, MT 149 6159 5310 28825 1213 7.502 0.972 0.386

Binghamton, NY 246 7093 5535 28400 1034 7.423 1.085 0.515

Birmingham-Hoover, AL 1104 51878 33750 213000 1179 7.647 0.970 -0.211

Bloomington, IN 182 5381 3538 23100 1172 7.328 1.136 0.687

Bloomington-Normal, IL 162 7698 4268 24575 1348 7.653 0.958 0.712

BoiseCity-Nampa, ID 574 23479 18875 101075 1290 7.479 0.992 -0.245

Boston-Cambridge-Quincy, MA-NH 4484 280550 153750 1382500 1205 7.759 0.930 -0.813

Boulder, CO 287 16504 9513 87000 1270 7.650 0.970 0.470

Bremerton-Silverdale, WA 238 8128 6813 51525 950 7.431 1.088 0.567

Bridgeport-Stamford-Norwalk, CT 892 78101 45500 380500 1183 7.999 0.769 -0.029

Brownsville-Harlingen, TX 382 6836 6532 30400 903 7.163 1.203 0.263

Buffalo-NiagaraFalls, NY 1131 41466 27225 158000 1094 7.557 1.035 -0.160

Burlington-SouthBurlington, VT 207 9724 7929 40925 1324 7.561 0.931 0.186

Canton-Massillon, OH 408 12708 10700 48100 1213 7.384 1.048 -0.042

CapeCoral-FortMyers, FL 573 21443 21100 136500 1149 7.365 1.041 -0.328

CedarRapids, IA 251 11535 8286 42150 1313 7.599 0.945 0.292

Champaign-Urbana, IL 222 7530 4575 37275 1291 7.306 1.139 0.548

Charleston, WV 304 13520 7628 40900 1113 7.750 0.946 0.572

Charlotte-Gastonia-Concord, NC-SC 1612 112575 52075 332500 1343 7.934 0.826 -0.285

Chattanooga, TN-GA 511 19778 17050 84250 1231 7.479 0.985 -0.228

Chicago-Naperville-Joliet, IL-IN-WI 9474 494675 272750 2340000 1204 7.653 0.991 -1.190

Chico, CA 218 5717 6061 37450 936 7.255 1.137 0.412

Cincinnati-Middletown, OH-KY-IN 2130 94574 53300 348750 1232 7.615 1.003 -0.478

Cleveland-Elyria-Mentor, OH 2101 101402 53800 388000 1151 7.703 0.978 -0.381

Coeurd’Alene, ID 132 3899 4360 22925 1190 7.212 1.071 -0.024

ColoradoSprings, CO 604 22581 16600 127750 1184 7.383 1.087 -0.022

Columbia, SC 709 28344 20225 118750 1223 7.507 1.020 -0.111

Columbus, GA-AL 288 10265 6191 51500 928 7.556 1.075 0.679

Columbus, OH 1743 86089 56300 341750 1292 7.629 0.955 -0.548

CorpusChristi, TX 413 14643 10731 64825 1136 7.459 1.058 0.217

61

Table B.4: Data and Estimated City Characteristics (cont’d)



Dallas-FortWorth-Arlington, TX 6067 349575 195000 1565000 1295 7.689 0.951 -1.041

Davenport-Moline-RockIsl, IA-IL 375 15734 10488 49375 1131 7.688 0.952 0.351

Dayton, OH 840 33268 18975 123250 1125 7.598 1.029 0.054

Deltona-Daytona-Ormond, FL 495 12019 12625 78025 987 7.172 1.165 -0.070

Denver-Aurora-Broomfield, CO 2430 141075 75125 754500 1387 7.588 1.000 -0.617

DesMoines-WestDesMoines, IA 540 32351 18150 104425 1418 7.765 0.879 0.064

Detroit-Warren-Livonia, MI 4466 199875 119250 934750 1081 7.627 1.014 -0.778

Duluth, MN-WI 274 9359 6959 39150 1124 7.461 1.056 0.421

Durham-ChapelHill, NC 473 29531 11675 95050 1215 7.894 0.895 0.463

EauClaire, WI 157 5645 4742 20850 1331 7.425 0.998 0.248

ElPaso, TX 726 23903 16250 163250 1026 7.332 1.154 0.090

Erie, PA 279 8941 6948 32375 1116 7.469 1.046 0.381

Eugene-Springfield, OR 341 10888 9882 55850 1069 7.379 1.074 0.179

Evansville, IN-KY 349 15175 8434 48050 1096 7.733 0.962 0.523

Fargo, ND-MN 191 9104 7030 31625 1470 7.567 0.898 0.025

Fayetteville, NC 350 14065 7462 77925 1060 7.514 1.090 0.559

Fayetteville-Springd-Rog, AR-MO 427 16421 10020 66975 1396 7.404 1.069 0.112

Flint, MI 435 11748 9961 54575 1044 7.319 1.123 0.164

FortCollins-Loveland, CO 284 10246 8405 62275 1222 7.314 1.091 0.180

FortWayne, IN 407 16263 9900 52875 1184 7.613 1.000 0.333

Fresno, CA 889 27071 21800 142250 1044 7.355 1.114 -0.150

Gainesville, FL 254 9035 6540 44600 1221 7.378 1.084 0.379

GrandRapids-Wyoming, MI 773 32458 22150 134500 1248 7.530 1.011 -0.140

Greeley, CO 238 6649 4890 39525 1341 7.091 1.194 0.237

GreenBay, WI 300 13655 8099 45250 1255 7.656 0.966 0.448

Greensboro-HighPoint, NC 690 31718 23100 106250 1151 7.716 0.913 -0.042

Gulfport-Biloxi, MS 237 9128 6650 31723.089 1090 7.707 0.930 0.538

Hagerstown-Martinsburg, MD-WV 257 7474 7335 34325 1316 7.217 1.065 -0.391

Harrisburg-Carlisle, PA 526 26279 15900 108850 1292 7.622 0.975 0.124

Hartford-W and E Hartford, CT 1185 70031 40075 285750 1227 7.774 0.909 -0.190

Hickory-Lenoir-Morganton, NC 358 11617 8316 44850 1275 7.369 1.081 0.167

Holland-GrandHaven, MI 257 9101 5217 46050 1321 7.312 1.141 0.499

Honolulu, HI 902 45003 28425 281500 1175 7.545 1.032 -0.083

Houston-SugarLand-Baytown, TX 5529 359325 149250 1605000 1228 7.804 0.941 -0.790

Huntington-Ashland, WV-KY-OH 284 8774 6708 28625 1009 7.551 1.027 0.485

Huntsville, AL 382 17655 11250 61950 1348 7.598 0.965 0.174

Indianapolis-Carmel, IN 1680 91450 50500 346750 1267 7.721 0.939 -0.370

IowaCity, IA 146 6497 4036 31075 1299 7.497 1.034 0.722

Jackson, MI 162 4741 3612 20050 1103 7.375 1.097 0.666

Jacksonville, FL 1284 57619 41575 258250 1258 7.543 0.989 -0.465

Jacksonville, NC 162 6008 3065 39750 931 7.519 1.107 1.012

Janesville, WI 159 4856 4441 19425 1046 7.451 1.040 0.584

JohnsonCity, TN 192 5575 4466 20850 997 7.472 1.064 0.660

Johnstown, PA 146 3710 3264 15025 1219 7.224 1.118 0.391

Joplin, MO 170 5161 4725 18125 1220 7.390 1.025 0.261

Kalamazoo-Portage, MI 322 11246 8018 54800 1152 7.411 1.083 0.342

KansasCity, MO-KS 1970 95462 59225 360250 1298 7.630 0.964 -0.566

Knoxville, TN 675 27894 24025 113750 1028 7.655 0.944 -0.052

LaCrosse, WI-MN 131 4910 3732 17775 1341 7.455 1.005 0.493

Lafayette, LA 254 16222 8403 58200 1261 7.861 0.866 0.616

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Lancaster, PA 496 18342 14775 75575 1244 7.450 1.018 -0.107

Lansing-EastLansing, MI 455 17650 11350 89775 1150 7.462 1.078 0.268

Laredo, TX 229 5573 5192 25225 1090 7.232 1.136 0.315

LasVegas-Paradise, NV 1792 91456 59575 458000 1263 7.586 0.986 -0.530

Lexington-Fayette, KY 443 21499 14625 83150 1284 7.631 0.946 0.103

Los Angeles-L Beach-S Ana, CA 12817 683025 433750 3972500 1207 7.596 0.998 -1.441

Lubbock, TX 267 8788 8033 35175 1105 7.466 1.015 0.231

Lynchburg, VA 241 7897 5695 28250 1209 7.435 1.059 0.428

Madison, WI 551 31061 20325 127750 1404 7.651 0.914 -0.103

McAllen-Edinburg-Mission, TX 696 12419 13850 54400 1078 7.041 1.190 -0.510

Medford, OR 198 6091 8251 34200 982 7.386 0.983 -0.164

Memphis, TN-MS-AR 1272 61145 39400 258750 1163 7.660 0.967 -0.264

Milwaukee-Waukesha-W Allis, WI 1541 78537 40800 276500 1206 7.735 0.952 -0.248

Minneapolis-St.Paul-Bl., MN-WI 3181 182875 103200 797500 1315 7.686 0.947 -0.740

Mobile, AL 402 14009 10853 56200 1180 7.456 1.039 0.130

Modesto, CA 506 14674 13750 91375 1186 7.182 1.131 -0.281

Muskegon-NortonShores, MI 174 4635 5132 23025 1151 7.224 1.066 -0.150

Napa, CA 132 6876 4618 46325 1169 7.557 1.014 0.828

Naples-MarcoIsland, FL 311 14415 12000 102625 1186 7.449 1.025 0.160

New York-N NJ-L Isl, NY-NJ-PA 18897 1166000 609000 5540000 1164 7.784 0.930 -1.479

Niles-BentonHarbor, MI 160 5207 3442 24400 1095 7.421 1.098 0.787

Norwich-NewLondon, CT 265 12835 8498 66950 1243 7.548 1.007 0.422

Ocala, FL 317 7339 8088 41375 1066 7.143 1.136 -0.166

Ogden-Clearfield, UT 511 15400 11975 73375 1291 7.240 1.125 -0.136

OklahomaCity, OK 1181 51753 32475 227250 1225 7.554 1.019 -0.256

Omaha-CouncilBluffs, NE-IA 824 42101 24550 159000 1325 7.652 0.959 -0.098

Orlando-Kissimmee, FL 2003 98517 63775 514250 1299 7.530 1.011 -0.616

Oxnard-Th Oaks-Ventura, CA 793 34443 26950 224500 1295 7.376 1.053 -0.371

PalmBay-Melbourne-Titusv, FL 532 16982 14175 86725 1205 7.301 1.098 -0.134

Pensacola-FerryPass-Brent, FL 450 12945 10575 67700 1138 7.265 1.133 0.055

Peoria, IL 370 15944 8647 54125 1291 7.594 1.009 0.374

Philadel-Cam-Wil, PA-NJ-DE-MD 5813 314925 178750 1302500 1157 7.750 0.939 -0.932

Phoenix-Mesa-Scottsdale, AZ 4089 179325 142750 1029250 1257 7.443 1.022 -1.164

Pittsburgh, PA 2360 107675 65500 418750 1131 7.671 0.977 -0.506

Portland-S Portl-Biddeford, ME 512 23439 18675 110400 1294 7.520 0.969 -0.183

Portland-Vanc-Beav, OR-WA 2147 105034 62375 451500 1272 7.606 0.992 -0.549

Poughkeepsie-Newb-Middlet, NY 667 19865 19650 124000 1204 7.187 1.114 -0.540

Provo-Orem, UT 505 12487 10836 58375 1241 7.144 1.158 -0.218

Pueblo, CO 153 3612 3589 18725 1066 7.177 1.154 0.460

PuntaGorda, FL 152 3461 4492 27675 895 7.135 1.157 0.341

Racine, WI 198 6753 4027 24925 1202 7.455 1.084 0.694

Raleigh-Cary, NC 1021 49081 30550 212750 1379 7.540 0.995 -0.327

Reading, PA 399 13992 12075 61225 1300 7.368 1.023 -0.266

Reno-Sparks, NV 405 19833 14475 93025 1271 7.579 0.963 0.083

Richmond, VA 1201 58495 33100 235500 1260 7.633 0.987 -0.216

Riverside-S Bernard-Ontario, CA 4009 109250 108250 741000 1086 7.169 1.155 -1.194

Roanoke, VA 295 12060 9356 42050 1362 7.515 0.955 -0.012

Rochester, NY 1034 43501 26400 150500 1206 7.614 0.995 -0.150

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Name Pop GDP Cons Capital Hours lnAi ln γi ln gi(’000s) (m$) (m$) (m$) (Annual)

Rockford, IL 347 11746 8171 42100 1227 7.446 1.056 0.262

Sacramento-Arden-Arc-Rosev, CA 2070 90391 69250 581250 1111 7.485 1.042 -0.599

Saginaw-Sag Township N, MI 204 6461 5181 25950 991 7.509 1.047 0.642

St.Louis, MO-IL 2797 120875 73275 460500 1269 7.566 1.010 -0.695

Salem, OR 382 11301 9027 63600 1160 7.244 1.145 0.147

Salinas, CA 406 17801 13150 116000 1108 7.496 1.040 0.231

SaltLakeCity, UT 1083 57691 40825 245250 1382 7.611 0.925 -0.509

SanAntonio, TX 1957 74146 53200 323000 1155 7.496 1.039 -0.555

SanDiego-Carlsbad-S Marcos, CA 2957 158650 104000 1045000 1177 7.575 1.008 -0.712

SanFrancisco-Oakl-Frem, CA 4206 293150 181750 1627500 1227 7.778 0.891 -0.883

SanJose-Sunnyvale-StaClara, CA 1778 137975 74900 730000 1273 7.841 0.869 -0.390

SanLuisObispo-PasoRobles, CA 261 10093 9309 83125 1109 7.327 1.082 0.206

SantaCruz-Watsonville, CA 251 9547 10199 76625 1186 7.278 1.051 -0.202

SantaFe, NM 142 6360 6021 36250 1004 7.621 0.939 0.612

SantaRosa-Petaluma, CA 463 19457 17275 141000 1193 7.373 1.049 -0.141

Savannah, GA 325 12295 8880 55500 1167 7.477 1.045 0.322

Scranton-Wilkes-Barre, PA 549 18089 15200 68675 1070 7.502 1.024 0.024

Seattle-Tacoma-Bellevue, WA 3274 202025 128000 992500 1258 7.723 0.914 -0.802

SiouxFalls, SD 224 13177 7905 48325 1584 7.636 0.902 0.235

SouthBend-Mishawaka, IN-MI 316 11807 7571 41625 1187 7.541 1.029 0.416

Spokane, WA 452 16456 14875 74225 1219 7.426 1.005 -0.226

Springfield, IL 206 8049 5224 33025 1138 7.551 1.030 0.657

Springfield, MA 687 21010 18075 106400 1107 7.335 1.096 -0.174

Springfield, MO 414 13598 12750 53375 1255 7.383 1.010 -0.320

Stockton, CA 665 18548 17275 121250 1052 7.218 1.152 -0.162

Syracuse, NY 645 25158 16350 93400 1123 7.592 1.012 0.106

Tallahassee, FL 350 12234 8531 60250 1301 7.335 1.088 0.118

Tampa-St.Petersb-Clearwater, FL 2693 107575 83950 500500 1187 7.491 1.017 -0.836

Toledo, OH 652 25597 16875 95175 1159 7.571 1.014 0.062

Topeka, KS 228 8136 5129 30000 1323 7.423 1.067 0.466

Trenton-Ewing, NJ 364 22767 12400 102475 1238 7.774 0.913 0.413

Tucson, AZ 983 29976 23750 168500 1068 7.319 1.130 -0.211

Tulsa, OK 898 41612 24175 168250 1303 7.577 1.005 -0.122

Tuscaloosa, AL 203 7598 4863 32550 1269 7.434 1.070 0.566

Utica-Rome, NY 294 8256 7021 33325 1061 7.381 1.087 0.332

Vineland-Millville-Bridgeton, NJ 155 4726 4226 20825 1085 7.395 1.061 0.549

VirginiaBeach-Norf-Newp, VA-NC 1657 72609 42475 362500 1204 7.520 1.053 -0.356

Visalia-Porterville, CA 416 10626 8933 58875 1042 7.228 1.164 0.171

Waterloo-CedarFalls, IA 163 7018 4393 21725 1271 7.632 0.967 0.697

Wausau, WI 129 5379 4010 17800 1360 7.543 0.955 0.498

Wichita, KS 593 25810 16400 88275 1235 7.624 0.976 0.071

Winston-Salem, NC 457 21390 14225 64750 1269 7.697 0.916 0.128

Worcester, MA 781 26898 22275 143250 1178 7.352 1.078 -0.289

Yakima, WA 231 6877 5143 30400 1028 7.410 1.101 0.592

York-Hanover, PA 416 14247 10681 65325 1169 7.406 1.075 0.159

Youngstown-War-Boardm, OH-PA 573 17030 15000 66275 948 7.504 1.044 0.097

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Urban Accounting and Welfare - NUS · Urban Accounting and Welfare Klaus Desmet Universidad Carlos...

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