Post on 12-Jun-2020
transcript
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)
Counterfactual Utility = 10.0191, Reallocation = 0.19913
ActualAvg. Amenities
11 12 13 14 15 16 17-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 10.0886, Reallocation = 0.4399
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)
Counterfactual Utility = 10.0607, Reallocation = 0.45742
ActualEfficiency Only
11 12 13 14 15 16 17-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 10.291, Reallocation = 0.63351
ActualAmenities Only
11 12 13 14 15 16 17-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 10.05, Reallocation = 0.14572
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)
Counterfactual Utility = 10.1094, Reallocation = 0.37565
ActualAvg. Efficiency
8 10 12 14 16 18-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 10.0189, Reallocation = 0.21897
ActualAvg. Amenities
11 12 13 14 15 16 17-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 10.0963, Reallocation = 0.47717
ActualAvg. Exc. Frictions
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
latio
n)
Counterfactual Utility = 10.0784, Reallocation = 0.40752
ActualAvg. Efficiency
8 10 12 14 16 18-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 10.0324, Reallocation = 0.30766
ActualAvg. Amenities
8 10 12 14 16 18-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 9.9585, Reallocation = 0.49123
ActualAvg. Exc. Frictions
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
-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(p
rob
> po
pula
tion)
Counterfactual Utility = 14.6992, Reallocation = 0.64395
ActualAvg. Efficiency
8 10 12 14 16 18-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 11.2977, Reallocation = 0.5001
ActualAvg. Amenities
12 13 14 15 16 17-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
Counterfactual Utility = 9.8496, Reallocation = 0.070892
ActualAvg. Exc. Frictions
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
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> po
pula
tion)
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.
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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
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
‐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
Change in Population
Cities with Smallest Percentage Change in City Population Without Amenity Differences
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
Seattle‐Tacoma‐Bellevue
Iowa City
San Diego
‐Carlsbad
‐San
Marcos
Salt Lake City
Billings
Tampa‐St. Petersburg‐Clearwater
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
Bremerton‐Silverdale
Tuscaloosa
Augusta‐Richmond County
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
Allentown‐Bethlehem
‐Easton
Anderson
Springfield
Colorado Springs
Utica‐Rome
Jackson
Vinelan
d‐M
illville‐Bridgeton
Bakersfield
Gainesville
Eau Claire
El Paso
Fresno
Eugene‐Springfield
Hickory‐Len
oir‐M
organ
ton
Can
ton‐M
assillon
Bloomington
Oxnard‐Thousand Oaks‐Ven
tura
Holland‐Grand Haven
Joplin
Tucson
Savannah
Worcester
Flint
Cham
paign
‐Urbana
Springfield
Tallahassee
Cap
e Coral‐Fort M
yers
St. Louis
Santa Cruz‐Watsonville
Reading
Fort Collins‐Loveland
Palm Bay‐M
elbourne‐Titusville
Pen
sacola‐Ferry Pass‐Brent
Bellingham
Med
ford
Chico
Visalia‐Porterville
Asheville
Salinas
Stockton
Laredo
Brownsville‐Harlingen
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
Muskegon‐Norton Shores
Coeu
r d'Alene
Hagerstown‐M
artinsburg
McAllen‐Edinburg‐M
ission
Percentage
Change in Population
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
Seattle‐Tacoma‐Bellevue
Iowa City
San Diego
‐Carlsbad
‐San
Marcos
Salt Lake City
Billings
Tampa‐St. Petersburg‐Clearwater
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
Bremerton‐Silverdale
Tuscaloosa
Augusta‐Richmond County
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
Allentown‐Bethlehem
‐Easton
Anderson
Springfield
Colorado Springs
Utica‐Rome
Jackson
Vinelan
d‐M
illville‐Bridgeton
Bakersfield
Gainesville
Eau Claire
El Paso
Fresno
Eugene‐Springfield
Hickory‐Len
oir‐M
organ
ton
Can
ton‐M
assillon
Bloomington
Oxnard‐Thousand Oaks‐Ven
tura
Holland‐Grand Haven
Joplin
Tucson
Savannah
Worcester
Flint
Cham
paign
‐Urbana
Springfield
Tallahassee
Cap
e Coral‐Fort M
yers
St. Louis
Santa Cruz‐Watsonville
Reading
Fort Collins‐Loveland
Palm Bay‐M
elbourne‐Titusville
Pen
sacola‐Ferry Pass‐Brent
Bellingham
Med
ford
Chico
Visalia‐Porterville
Asheville
Salinas
Stockton
Laredo
Brownsville‐Harlingen
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
Muskegon‐Norton Shores
Coeu
r d'Alene
Hagerstown‐M
artinsburg
McAllen‐Edinburg‐M
ission
Percentage
Change in Population
Cities with Largest Percentage Change in City Population Without Efficiency Differences
‐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
Minneapolis‐St. Pau
l‐…
Dallas‐Fort W
orth‐…
Daven
port‐M
oline‐…
Mad
ison
South Ben
d‐M
ishaw
aka
Cleveland‐Elyria‐Men
tor
Beaumont‐Port Arthur
Knoxville
Pittsburgh
Mem
phis
Bloomington‐Norm
alOmah
a‐Council Bluffs
Green
Bay
Boulder
Lexington‐Fayette
Birmingham
‐Hoover
Santa Rosa‐Petaluma
Chicago‐Nap
erville‐…
Columbus
San Antonio
Kan
sas City
Waterloo‐Ced
ar Falls
Richmond
Wichita
Harrisburg‐Carlisle
Ced
ar Rap
ids
Detroit‐W
arren‐Livonia
Rochester
Cincinnati‐Middletown
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
Huntington‐Ashland
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
Change in Population
Cities with Smallest Percentage Change in City Population Without Efficiency Differences
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
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐100%
100%
300%
500%
700%
900%
1100%
1300%
1500%
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Ren
o‐Sparks
Des Moines‐W
est Des Moines
Toledo
Wichita
Tallahassee
Dayton
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Burlington‐South Burlington
Youngstown‐W
arren‐Boardman
Mobile
El Paso
Naples‐Marco Island
Winston‐Salem
Syracuse
Salinas
Harrisburg‐Carlisle
Fort Collins‐Loveland
Eau Claire
Hickory‐Len
oir‐M
organton
York‐Hanover
Baton Rouge
Eugene‐Springfield
Santa Cruz‐Watsonville
Flint
Huntsville
Visalia‐Porterville
Amarillo
Joplin
Augusta‐Richmond County
South Ben
d‐M
ishaw
aka
Greeley
Lubbock
Corpus Christi
Salt Lake City
Appleton
Rockford
Ced
ar Rapids
Punta Gorda
Brownsville‐Harlingen
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
Beaumont‐Port Arthur
Peoria
Pueblo
Lynchburg
Norw
ich‐New London
Duluth
Spokane
La Crosse
Trenton‐Ewing
Wausau
Topeka
Green
Bay
Boulder
Ann Arbor
Huntington‐Ashland
Holland‐Grand Haven
Durham
‐Chapel Hill
Vineland‐M
illville‐Bridgeton
Bingham
ton
Gulfport‐Biloxi
Cham
paign
‐Urbana
Evansville
Janesville
Tuscaloosa
Bremerton‐Silverdale
Santa Rosa‐Petaluma
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
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐100%
100%
300%
500%
700%
900%
1100%
1300%
1500%
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Ren
o‐Sparks
Des Moines‐W
est Des Moines
Toledo
Wichita
Tallahassee
Dayton
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Burlington‐South Burlington
Youngstown‐W
arren‐Boardman
Mobile
El Paso
Naples‐Marco Island
Winston‐Salem
Syracuse
Salinas
Harrisburg‐Carlisle
Fort Collins‐Loveland
Eau Claire
Hickory‐Len
oir‐M
organton
York‐Hanover
Baton Rouge
Eugene‐Springfield
Santa Cruz‐Watsonville
Flint
Huntsville
Visalia‐Porterville
Amarillo
Joplin
Augusta‐Richmond County
South Ben
d‐M
ishaw
aka
Greeley
Lubbock
Corpus Christi
Salt Lake City
Appleton
Rockford
Ced
ar Rapids
Punta Gorda
Brownsville‐Harlingen
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
Beaumont‐Port Arthur
Peoria
Pueblo
Lynchburg
Norw
ich‐New London
Duluth
Spokane
La Crosse
Trenton‐Ewing
Wausau
Topeka
Green
Bay
Boulder
Ann Arbor
Huntington‐Ashland
Holland‐Grand Haven
Durham
‐Chapel Hill
Vineland‐M
illville‐Bridgeton
Bingham
ton
Gulfport‐Biloxi
Cham
paign
‐Urbana
Evansville
Janesville
Tuscaloosa
Bremerton‐Silverdale
Santa Rosa‐Petaluma
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
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
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
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Ren
o‐Sparks
Des Moines‐W
est Des Moines
Toledo
Wichita
Tallahassee
Dayton
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Burlington‐South Burlington
Youngstown‐W
arren‐Boardman
Mobile
El Paso
Naples‐Marco Island
Winston‐Salem
Syracuse
Salinas
Harrisburg‐Carlisle
Fort Collins‐Loveland
Eau Claire
Hickory‐Len
oir‐M
organton
York‐Hanover
Baton Rouge
Eugene‐Springfield
Santa Cruz‐Watsonville
Flint
Huntsville
Visalia‐Porterville
Amarillo
Joplin
Augusta‐Richmond County
South Ben
d‐M
ishaw
aka
Greeley
Lubbock
Corpus Christi
Salt Lake City
Appleton
Rockford
Ced
ar Rapids
Punta Gorda
Brownsville‐Harlingen
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
Beaumont‐Port Arthur
Peoria
Pueblo
Lynchburg
Norw
ich‐New London
Duluth
Spokane
La Crosse
Trenton‐Ewing
Wausau
Topeka
Green
Bay
Boulder
Ann Arbor
Huntington‐Ashland
Holland‐Grand Haven
Durham
‐Chapel Hill
Vineland‐M
illville‐Bridgeton
Bingham
ton
Gulfport‐Biloxi
Cham
paign
‐Urbana
Evansville
Janesville
Tuscaloosa
Bremerton‐Silverdale
Santa Rosa‐Petaluma
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
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐40%
‐20%
0%
20%
40%
60%
80%
ntage Chan
ge in
Population
Cities with Smallest Percentage Change in City Population Without Excessive Friction Differences
‐100%
100%
300%
500%
700%
900%
1100%
1300%
1500%
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Ren
o‐Sparks
Des Moines‐W
est Des Moines
Toledo
Wichita
Tallahassee
Dayton
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Burlington‐South Burlington
Youngstown‐W
arren‐Boardman
Mobile
El Paso
Naples‐Marco Island
Winston‐Salem
Syracuse
Salinas
Harrisburg‐Carlisle
Fort Collins‐Loveland
Eau Claire
Hickory‐Len
oir‐M
organton
York‐Hanover
Baton Rouge
Eugene‐Springfield
Santa Cruz‐Watsonville
Flint
Huntsville
Visalia‐Porterville
Amarillo
Joplin
Augusta‐Richmond County
South Ben
d‐M
ishaw
aka
Greeley
Lubbock
Corpus Christi
Salt Lake City
Appleton
Rockford
Ced
ar Rapids
Punta Gorda
Brownsville‐Harlingen
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
Beaumont‐Port Arthur
Peoria
Pueblo
Lynchburg
Norw
ich‐New London
Duluth
Spokane
La Crosse
Trenton‐Ewing
Wausau
Topeka
Green
Bay
Boulder
Ann Arbor
Huntington‐Ashland
Holland‐Grand Haven
Durham
‐Chapel Hill
Vineland‐M
illville‐Bridgeton
Bingham
ton
Gulfport‐Biloxi
Cham
paign
‐Urbana
Evansville
Janesville
Tuscaloosa
Bremerton‐Silverdale
Santa Rosa‐Petaluma
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
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐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
Cities with Smallest Percentage Change in City Population Without Excessive Friction Differences
‐100%
100%
300%
500%
700%
900%
1100%
1300%
1500%
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Ren
o‐Sparks
Des Moines‐W
est Des Moines
Toledo
Wichita
Tallahassee
Dayton
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Burlington‐South Burlington
Youngstown‐W
arren‐Boardman
Mobile
El Paso
Naples‐Marco Island
Winston‐Salem
Syracuse
Salinas
Harrisburg‐Carlisle
Fort Collins‐Loveland
Eau Claire
Hickory‐Len
oir‐M
organton
York‐Hanover
Baton Rouge
Eugene‐Springfield
Santa Cruz‐Watsonville
Flint
Huntsville
Visalia‐Porterville
Amarillo
Joplin
Augusta‐Richmond County
South Ben
d‐M
ishaw
aka
Greeley
Lubbock
Corpus Christi
Salt Lake City
Appleton
Rockford
Ced
ar Rapids
Punta Gorda
Brownsville‐Harlingen
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
Beaumont‐Port Arthur
Peoria
Pueblo
Lynchburg
Norw
ich‐New London
Duluth
Spokane
La Crosse
Trenton‐Ewing
Wausau
Topeka
Green
Bay
Boulder
Ann Arbor
Huntington‐Ashland
Holland‐Grand Haven
Durham
‐Chapel Hill
Vineland‐M
illville‐Bridgeton
Bingham
ton
Gulfport‐Biloxi
Cham
paign
‐Urbana
Evansville
Janesville
Tuscaloosa
Bremerton‐Silverdale
Santa Rosa‐Petaluma
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
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐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
McAllen‐Edinburg‐M
ission
Denver‐Aurora‐Broomfield
Sacram
ento‐Arden
‐ …Kansas City
San Antonio
Columbus
San Diego
‐Carlsbad
‐San
…Portland‐Vancouver‐…
Las Vegas‐Paradise
Jacksonville
Pittsburgh
Cincinnati‐Middletown
St. Louis
Austin‐Round Rock
Oxnard‐Thousand Oaks‐…
Cape Coral‐Fort M
yers
Muskegon‐Norton Shores
Reading
Santa Fe
Medford
San Luis Obispo‐Paso …
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
Allentown‐Bethlehem
‐ …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
Buffalo‐Niagara Falls
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
Cities with Smallest Percentage Change in City Population Without Excessive Friction Differences
Figure A3: Changes in Population Sizes with Average Excessive Frictions
44
150%
180%
210%
240%Population
Cities with Largest Percentage Change in City Population Without Amenity Differences
‐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
Cities with Largest Percentage Change in City Population Without Amenity Differences
‐30%
0%
30%
60%
90%
120%
150%
180%
210%
240%
Columbia
Lubbock
Tampa‐St. Petersburg‐Clearwater
Dayton
Albuquerque
Oklahoma City
Springfield
Akron
Napa
Orlando‐Kissimmee
Toledo
Grand Rapids‐Wyoming
La Crosse
Syracuse
Salem
Detroit‐W
arren‐Livonia
San Francisco‐Oakland‐Fremont
Norw
ich‐New London
Peoria
Eau Claire
Baltimore‐Towson
Tulsa
Austin‐Round Rock
Cincinnati‐Middletown
Denver‐Aurora‐Broomfield
Atlanta‐Sandy Springs‐M
arietta
Fort W
ayne
Los Angeles‐Long Beach‐Santa Ana
Raleigh
‐Cary
Albany‐Schenectady‐Troy
Rochester
Boise City‐Nam
pa
Portland‐Vancouver‐Beaverton
Amarillo
Chicago‐Naperville‐Joliet
Jacksonville
Richmond
Las Vegas‐Paradise
Chattanooga
Cleveland‐Elyria‐Mentor
Pittsburgh
Medford
Wichita
Harrisburg‐Carlisle
Boulder
Birmingham
‐Hoover
Memphis
Beaumont‐Port Arthur
Green
Bay
Evansville
Waterloo‐Ced
ar Falls
Billings
Kansas City
Huntsville
Portland‐South Portland‐Biddeford
Omaha‐Council Bluffs
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
Indianapolis‐Carmel
Appleton
Knoxville
ew York‐Northern New Jersey‐Long Island
Lexington‐Fayette
Wausau
Boston‐Cam
bridge‐Quincy
Roanoke
Ced
ar Rapids
Gulfport‐Biloxi
Santa Rosa‐Petaluma
Trenton‐Ewing
Durham
‐Chapel Hill
Hartford‐W
est Hartford‐East Hartford
Sioux Falls
Winston‐Salem
Green
sboro‐High Point
Bangor
San Antonio
Burlington‐South Burlington
Madison
San Jose‐Sunnyvale‐Santa Clara
Lafayette
San Luis Obispo‐Paso Robles
Des Moines‐W
est Des Moines
South Ben
d‐M
ishaw
aka
Charlotte‐Gastonia‐Concord
Fargo
Bridgeport‐Stamford‐Norw
alk
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Amenity Differences
‐30%
0%
30%
60%
90%
120%
150%
180%
210%
240%
Columbia
Lubbock
Tampa‐St. Petersburg‐Clearwater
Dayton
Albuquerque
Oklahoma City
Springfield
Akron
Napa
Orlando‐Kissimmee
Toledo
Grand Rapids‐Wyoming
La Crosse
Syracuse
Salem
Detroit‐W
arren‐Livonia
San Francisco‐Oakland‐Fremont
Norw
ich‐New London
Peoria
Eau Claire
Baltimore‐Towson
Tulsa
Austin‐Round Rock
Cincinnati‐Middletown
Denver‐Aurora‐Broomfield
Atlanta‐Sandy Springs‐M
arietta
Fort W
ayne
Los Angeles‐Long Beach‐Santa Ana
Raleigh
‐Cary
Albany‐Schenectady‐Troy
Rochester
Boise City‐Nam
pa
Portland‐Vancouver‐Beaverton
Amarillo
Chicago‐Naperville‐Joliet
Jacksonville
Richmond
Las Vegas‐Paradise
Chattanooga
Cleveland‐Elyria‐Mentor
Pittsburgh
Medford
Wichita
Harrisburg‐Carlisle
Boulder
Birmingham
‐Hoover
Memphis
Beaumont‐Port Arthur
Green
Bay
Evansville
Waterloo‐Ced
ar Falls
Billings
Kansas City
Huntsville
Portland‐South Portland‐Biddeford
Omaha‐Council Bluffs
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
Indianapolis‐Carmel
Appleton
Knoxville
New York‐Northern New Jersey‐Long Island
Lexington‐Fayette
Wausau
Boston‐Cam
bridge‐Quincy
Roanoke
Ced
ar Rapids
Gulfport‐Biloxi
Santa Rosa‐Petaluma
Trenton‐Ewing
Durham
‐Chapel Hill
Hartford‐W
est Hartford‐East Hartford
Sioux Falls
Winston‐Salem
Green
sboro‐High Point
Bangor
San Antonio
Burlington‐South Burlington
Madison
San Jose‐Sunnyvale‐Santa Clara
Lafayette
San Luis Obispo‐Paso Robles
Des Moines‐W
est Des Moines
South Ben
d‐M
ishaw
aka
Charlotte‐Gastonia‐Concord
Fargo
Bridgeport‐Stamford‐Norw
alk
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Amenity Differences
0%
Cities with Smallest Percentage Change in City Population Without Amenity Differences
‐30%
0%
30%
60%
90%
120%
150%
180%
210%
240%
Columbia
Lubbock
Tampa‐St. Petersburg‐Clearwater
Dayton
Albuquerque
Oklahoma City
Springfield
Akron
Napa
Orlando‐Kissimmee
Toledo
Grand Rapids‐Wyoming
La Crosse
Syracuse
Salem
Detroit‐W
arren‐Livonia
San Francisco‐Oakland‐Fremont
Norw
ich‐New London
Peoria
Eau Claire
Baltimore‐Towson
Tulsa
Austin‐Round Rock
Cincinnati‐Middletown
Denver‐Aurora‐Broomfield
Atlanta‐Sandy Springs‐M
arietta
Fort W
ayne
Los Angeles‐Long Beach‐Santa Ana
Raleigh
‐Cary
Albany‐Schenectady‐Troy
Rochester
Boise City‐Nam
pa
Portland‐Vancouver‐Beaverton
Amarillo
Chicago‐Naperville‐Joliet
Jacksonville
Richmond
Las Vegas‐Paradise
Chattanooga
Cleveland‐Elyria‐Mentor
Pittsburgh
Medford
Wichita
Harrisburg‐Carlisle
Boulder
Birmingham
‐Hoover
Memphis
Beaumont‐Port Arthur
Green
Bay
Evansville
Waterloo‐Ced
ar Falls
Billings
Kansas City
Huntsville
Portland‐South Portland‐Biddeford
Omaha‐Council Bluffs
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
Indianapolis‐Carmel
Appleton
Knoxville
New York‐Northern New Jersey‐Long Island
Lexington‐Fayette
Wausau
Boston‐Cam
bridge‐Quincy
Roanoke
Ced
ar Rapids
Gulfport‐Biloxi
Santa Rosa‐Petaluma
Trenton‐Ewing
Durham
‐Chapel Hill
Hartford‐W
est Hartford‐East Hartford
Sioux Falls
Winston‐Salem
Green
sboro‐High Point
Bangor
San Antonio
Burlington‐South Burlington
Madison
San Jose‐Sunnyvale‐Santa Clara
Lafayette
San Luis Obispo‐Paso Robles
Des Moines‐W
est Des Moines
South Ben
d‐M
ishaw
aka
Charlotte‐Gastonia‐Concord
Fargo
Bridgeport‐Stamford‐Norw
alk
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Amenity Differences
‐60%
‐40%
‐20%
0%
ntage Chan
ge in
Population
Cities with Smallest Percentage Change in City Population Without Amenity Differences
‐30%
0%
30%
60%
90%
120%
150%
180%
210%
240%
Columbia
Lubbock
Tampa‐St. Petersburg‐Clearwater
Dayton
Albuquerque
Oklahoma City
Springfield
Akron
Napa
Orlando‐Kissimmee
Toledo
Grand Rapids‐Wyoming
La Crosse
Syracuse
Salem
Detroit‐W
arren‐Livonia
San Francisco‐Oakland‐Fremont
Norw
ich‐New London
Peoria
Eau Claire
Baltimore‐Towson
Tulsa
Austin‐Round Rock
Cincinnati‐Middletown
Denver‐Aurora‐Broomfield
Atlanta‐Sandy Springs‐M
arietta
Fort W
ayne
Los Angeles‐Long Beach‐Santa Ana
Raleigh
‐Cary
Albany‐Schenectady‐Troy
Rochester
Boise City‐Nam
pa
Portland‐Vancouver‐Beaverton
Amarillo
Chicago‐Naperville‐Joliet
Jacksonville
Richmond
Las Vegas‐Paradise
Chattanooga
Cleveland‐Elyria‐Mentor
Pittsburgh
Medford
Wichita
Harrisburg‐Carlisle
Boulder
Birmingham
‐Hoover
Memphis
Beaumont‐Port Arthur
Green
Bay
Evansville
Waterloo‐Ced
ar Falls
Billings
Kansas City
Huntsville
Portland‐South Portland‐Biddeford
Omaha‐Council Bluffs
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
Indianapolis‐Carmel
Appleton
Knoxville
New York‐Northern New Jersey‐Long Island
Lexington‐Fayette
Wausau
Boston‐Cam
bridge‐Quincy
Roanoke
Ced
ar Rapids
Gulfport‐Biloxi
Santa Rosa‐Petaluma
Trenton‐Ewing
Durham
‐Chapel Hill
Hartford‐W
est Hartford‐East Hartford
Sioux Falls
Winston‐Salem
Green
sboro‐High Point
Bangor
San Antonio
Burlington‐South Burlington
Madison
San Jose‐Sunnyvale‐Santa Clara
Lafayette
San Luis Obispo‐Paso Robles
Des Moines‐W
est Des Moines
South Ben
d‐M
ishaw
aka
Charlotte‐Gastonia‐Concord
Fargo
Bridgeport‐Stamford‐Norw
alk
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Amenity Differences
‐100%
‐80%
‐60%
‐40%
‐20%
0%
Johnstown
gon‐Norton Shores
a Cruz‐Watsonville
Springfield
Visalia‐Porterville
Colorado Springs
Utica‐Rome
Eugene‐Springfield
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
nia Beach‐Norfolk‐…
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
Cities with Smallest Percentage Change in City Population Without Amenity Differences
‐30%
0%
30%
60%
90%
120%
150%
180%
210%
240%
Columbia
Lubbock
Tampa‐St. Petersburg‐Clearwater
Dayton
Albuquerque
Oklahoma City
Springfield
Akron
Napa
Orlando‐Kissimmee
Toledo
Grand Rapids‐Wyoming
La Crosse
Syracuse
Salem
Detroit‐W
arren‐Livonia
San Francisco‐Oakland‐Fremont
Norw
ich‐New London
Peoria
Eau Claire
Baltimore‐Towson
Tulsa
Austin‐Round Rock
Cincinnati‐Middletown
Denver‐Aurora‐Broomfield
Atlanta‐Sandy Springs‐M
arietta
Fort W
ayne
Los Angeles‐Long Beach‐Santa Ana
Raleigh
‐Cary
Albany‐Schenectady‐Troy
Rochester
Boise City‐Nam
pa
Portland‐Vancouver‐Beaverton
Amarillo
Chicago‐Naperville‐Joliet
Jacksonville
Richmond
Las Vegas‐Paradise
Chattanooga
Cleveland‐Elyria‐Mentor
Pittsburgh
Medford
Wichita
Harrisburg‐Carlisle
Boulder
Birmingham
‐Hoover
Memphis
Beaumont‐Port Arthur
Green
Bay
Evansville
Waterloo‐Ced
ar Falls
Billings
Kansas City
Huntsville
Portland‐South Portland‐Biddeford
Omaha‐Council Bluffs
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
Indianapolis‐Carmel
Appleton
Knoxville
New York‐Northern New Jersey‐Long Island
Lexington‐Fayette
Wausau
Boston‐Cam
bridge‐Quincy
Roanoke
Ced
ar Rapids
Gulfport‐Biloxi
Santa Rosa‐Petaluma
Trenton‐Ewing
Durham
‐Chapel Hill
Hartford‐W
est Hartford‐East Hartford
Sioux Falls
Winston‐Salem
Green
sboro‐High Point
Bangor
San Antonio
Burlington‐South Burlington
Madison
San Jose‐Sunnyvale‐Santa Clara
Lafayette
San Luis Obispo‐Paso Robles
Des Moines‐W
est Des Moines
South Ben
d‐M
ishaw
aka
Charlotte‐Gastonia‐Concord
Fargo
Bridgeport‐Stamford‐Norw
alk
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Amenity Differences
‐100%
‐80%
‐60%
‐40%
‐20%
0%
Johnstown
Muskegon‐Norton Shores
Santa Cruz‐Watsonville
Springfield
Visalia‐Porterville
Colorado Springs
Utica‐Rome
Eugene‐Springfield
Gainesville
Jackson
Savannah
Hickory‐Len
oir‐M
organton
Cape Coral‐Fort M
yers
Anderson
Bakersfield
Fresno
Bellingham
Worcester
Tallahassee
Holland‐Grand Haven
Cham
paign
‐Urbana
Palm Bay‐M
elbourne‐…
El Paso
Bloomington
Asheville
Santa Fe
Pensacola‐Ferry Pass‐Brent
Chico
Tucson
Flint
Fort Collins‐Loveland
Salinas
Ogden
‐Clearfield
Laredo
Stockton
Hagerstown‐M
artinsburg
Brownsville‐Harlingen
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
Augusta‐Richmond County
Bingham
ton
Bremerton‐Silverdale
York‐Hanover
Allentown‐Bethlehem
‐…Fayetteville‐Springdale‐…
Oxnard‐Thousand Oaks‐…
Vineland‐M
illville‐Bridgeton
Racine
Topeka
Jacksonville
Tuscaloosa
Canton‐M
assillon
Lansing‐East Lansing
Fayetteville
Lynchburg
Rockford
Johnson City
Corpus Christi
Duluth
McAllen‐Edinburg‐M
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
Naples‐Marco Island
Phoenix‐M
esa‐Scottsdale
St. Louis
Buffalo‐Niagara Falls
Honolulu
Lancaster
Seattle‐Tacoma‐Bellevue
Spokane
Springfield
Huntington‐Ashland
Ann Arbor
Percentage
Chan
ge in
Population
Cities with Smallest Percentage Change in City Population Without Amenity Differences
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
Seattle‐Tacoma‐Bellevue
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
‐Arcade‐Roseville
Mobile
Tuscaloosa
Tampa‐St. Petersburg‐Clearwater
Rockford
Bremerton‐Silverdale
Niles‐Ben
ton Harbor
Nap
les‐Marco Island
Lynchburg
Bingham
ton
Lancaster
Topeka
Yakima
Augusta‐Richmond County
Kalam
azoo‐Portage
Eau Claire
York‐Han
over
Anderson
Vinelan
d‐M
illville‐Bridgeton
Fayetteville‐Springdale‐Rogers
Jackson
Springfield
Utica‐Rome
Gainesville
Allentown‐Bethlehem
‐Easton
Colorado Springs
Phoen
ix‐M
esa‐Scottsdale
Eugene‐Springfield
Bakersfield
Joplin
Bloomington
Hickory‐Len
oir‐M
organ
ton
El Paso
Can
ton‐M
assillon
Fresno
Holland‐Grand Haven
Cham
paign
‐Urbana
Savannah
Oxnard‐Thousand Oaks‐Ven
tura
Flint
Worcester
Tallahassee
Tucson
Springfield
St. Louis
Santa Cruz‐Watsonville
Cap
e Coral‐Fort M
yers
Fort Collins‐Loveland
Reading
Med
ford
Bellingham
Palm Bay‐M
elbourne‐Titusville
Chico
Pen
sacola‐Ferry Pass‐Brent
Asheville
Visalia‐Porterville
Salinas
Laredo
Brownsville‐Harlingen
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
Muskegon‐Norton Shores
Coeu
r d'Alene
Hagerstown‐M
artinsburg
McAllen‐Edinburg‐M
ission
Percentage
Change in Population
Cities with Largest Percentage Change in City Population Without Efficiency Differences
0%
20%
on
Cities with Smallest Percentage Change in City Population Without Efficiency Differences
‐100%
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
Amarillo
Orlan
do‐Kissimmee
Youngstown‐W
arren‐Boardman
Seattle‐Tacoma‐Bellevue
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
‐Arcade‐Roseville
Mobile
Tuscaloosa
Tampa‐St. Petersburg‐Clearwater
Rockford
Bremerton‐Silverdale
Niles‐Ben
ton Harbor
Nap
les‐Marco Island
Lynchburg
Bingham
ton
Lancaster
Topeka
Yakima
Augusta‐Richmond County
Kalam
azoo‐Portage
Eau Claire
York‐Han
over
Anderson
Vinelan
d‐M
illville‐Bridgeton
Fayetteville‐Springdale‐Rogers
Jackson
Springfield
Utica‐Rome
Gainesville
Allentown‐Bethlehem
‐Easton
Colorado Springs
Phoen
ix‐M
esa‐Scottsdale
Eugene‐Springfield
Bakersfield
Joplin
Bloomington
Hickory‐Len
oir‐M
organ
ton
El Paso
Can
ton‐M
assillon
Fresno
Holland‐Grand Haven
Cham
paign
‐Urbana
Savannah
Oxnard‐Thousand Oaks‐Ven
tura
Flint
Worcester
Tallahassee
Tucson
Springfield
St. Louis
Santa Cruz‐Watsonville
Cap
e Coral‐Fort M
yers
Fort Collins‐Loveland
Reading
Med
ford
Bellingham
Palm Bay‐M
elbourne‐Titusville
Chico
Pen
sacola‐Ferry Pass‐Brent
Asheville
Visalia‐Porterville
Salinas
Laredo
Brownsville‐Harlingen
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
Muskegon‐Norton Shores
Coeu
r d'Alene
Hagerstown‐M
artinsburg
McAllen‐Edinburg‐M
ission
Percentage
Change in Population
Cities with Largest Percentage Change in City Population Without Efficiency Differences
‐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
San Luis Obispo‐Paso …
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
Santa Rosa‐Petaluma
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
Minneapolis‐St. Pau
l‐…
Ced
ar Rap
ids
Cleveland‐Elyria‐Men
tor
Omah
a‐Council Bluffs
Mem
phis
Dallas‐Fort W
orth‐…
San Antonio
Birmingham
‐Hoover
Burlington‐South …
Pittsburgh
Harrisburg‐Carlisle
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
Cincinnati‐Middletown
Portland‐Van
couver‐…
Dayton
Detroit‐W
arren‐Livonia
Springfield
Tulsa
Norw
ich‐New
London
Las Vegas‐Parad
ise
Toledo
Huntington‐Ashland
Alban
y‐Schen
ectady‐…
Den
ver‐Aurora‐…
Columbus
Spokane
Roan
oke
Austin‐Round Rock
San Francisco‐Oakland‐…
Billings
Buffalo‐Niagara Falls
Oklah
oma City
Honolulu
Salem
Jacksonville
Los Angeles‐Long …
Baltimore‐Towson
Raleigh
‐Cary
Jacksonville
Portland‐South …
Saginaw
‐Saginaw
…Iowa City
Grand Rap
ids‐Wyoming
Fayetteville
Atlan
ta‐San
dy Springs‐…
Akron
Albuquerque
Percentage
Change in Population
Cities with Smallest Percentage Change in City Population Without Efficiency Differences
Figure A5: Changes in Population Sizes with Average Effi ciency (with Externalities)
46
700%
800%
900%ulation
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐100%
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
Knoxville
Green
sboro‐High Point
Bakersfield
Bellingham
Bangor
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Des Moines‐W
est Des Moines
Ren
o‐Sparks
Toledo
Wichita
Dayton
Tallahassee
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Youngstown‐W
arren‐Boardman
El Paso
Mobile
Syracuse
Winston‐Salem
Burlington‐South Burlington
Harrisburg‐Carlisle
Naples‐Marco Island
Salinas
Baton Rouge
Fort Collins‐Loveland
Hickory‐Len
oir‐M
organton
York‐Hanover
Flint
Eugene‐Springfield
Huntsville
Visalia‐Porterville
Augusta‐Richmond County
Santa Cruz‐Watsonville
Eau Claire
Amarillo
South Ben
d‐M
ishaw
aka
Joplin
Greeley
Lubbock
Corpus Christi
Salt Lake City
Rockford
Appleton
Brownsville‐Harlingen
Ced
ar Rapids
Lansing‐East Lansing
Laredo
Punta Gorda
Scranton‐W
ilkes‐Barre
Utica‐Rome
Kalam
azoo‐Portage
Fort W
ayne
Billings
Johnstown
Davenport‐M
oline‐Rock Island
Gainesville
Erie
Beaumont‐Port Arthur
Peoria
Chico
Norw
ich‐New London
Duluth
Spokane
Lynchburg
Trenton‐Ewing
Pueblo
Green
Bay
Topeka
La Crosse
Wausau
Boulder
Ann Arbor
Durham
‐Chapel Hill
Huntington‐Ashland
Holland‐Grand Haven
Bingham
ton
Vineland‐M
illville‐Bridgeton
Evansville
Gulfport‐Biloxi
Cham
paign
‐Urbana
Tuscaloosa
Bremerton‐Silverdale
Fayetteville
Janesville
Charleston
Yakima
Santa Rosa‐Petaluma
Lafayette
ginaw
‐Saginaw
Township North
Springfield
Johnson City
Jackson
Bloomington
Columbus
Waterloo‐Ced
ar Falls
Racine
Bloomington‐Norm
al
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐100%
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
Knoxville
Green
sboro‐High Point
Bakersfield
Bellingham
Bangor
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Des Moines‐W
est Des Moines
Ren
o‐Sparks
Toledo
Wichita
Dayton
Tallahassee
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Youngstown‐W
arren‐Boardman
El Paso
Mobile
Syracuse
Winston‐Salem
Burlington‐South Burlington
Harrisburg‐Carlisle
Naples‐Marco Island
Salinas
Baton Rouge
Fort Collins‐Loveland
Hickory‐Len
oir‐M
organton
York‐Hanover
Flint
Eugene‐Springfield
Huntsville
Visalia‐Porterville
Augusta‐Richmond County
Santa Cruz‐Watsonville
Eau Claire
Amarillo
South Ben
d‐M
ishaw
aka
Joplin
Greeley
Lubbock
Corpus Christi
Salt Lake City
Rockford
Appleton
Brownsville‐Harlingen
Ced
ar Rapids
Lansing‐East Lansing
Laredo
Punta Gorda
Scranton‐W
ilkes‐Barre
Utica‐Rome
Kalam
azoo‐Portage
Fort W
ayne
Billings
Johnstown
Davenport‐M
oline‐Rock Island
Gainesville
Erie
Beaumont‐Port Arthur
Peoria
Chico
Norw
ich‐New London
Duluth
Spokane
Lynchburg
Trenton‐Ewing
Pueblo
Green
Bay
Topeka
La Crosse
Wausau
Boulder
Ann Arbor
Durham
‐Chapel Hill
Huntington‐Ashland
Holland‐Grand Haven
Bingham
ton
Vineland‐M
illville‐Bridgeton
Evansville
Gulfport‐Biloxi
Cham
paign
‐Urbana
Tuscaloosa
Bremerton‐Silverdale
Fayetteville
Janesville
Charleston
Yakima
Santa Rosa‐Petaluma
Lafayette
Saginaw
‐Saginaw
Township North
Springfield
Johnson City
Jackson
Bloomington
Columbus
Waterloo‐Ced
ar Falls
Racine
Bloomington‐Norm
al
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
60%
80%
Cities with Smallest Percentage Change in City Population Without Excessive Friction Differences
‐100%
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
Knoxville
Green
sboro‐High Point
Bakersfield
Bellingham
Bangor
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Des Moines‐W
est Des Moines
Ren
o‐Sparks
Toledo
Wichita
Dayton
Tallahassee
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Youngstown‐W
arren‐Boardman
El Paso
Mobile
Syracuse
Winston‐Salem
Burlington‐South Burlington
Harrisburg‐Carlisle
Naples‐Marco Island
Salinas
Baton Rouge
Fort Collins‐Loveland
Hickory‐Len
oir‐M
organton
York‐Hanover
Flint
Eugene‐Springfield
Huntsville
Visalia‐Porterville
Augusta‐Richmond County
Santa Cruz‐Watsonville
Eau Claire
Amarillo
South Ben
d‐M
ishaw
aka
Joplin
Greeley
Lubbock
Corpus Christi
Salt Lake City
Rockford
Appleton
Brownsville‐Harlingen
Ced
ar Rapids
Lansing‐East Lansing
Laredo
Punta Gorda
Scranton‐W
ilkes‐Barre
Utica‐Rome
Kalam
azoo‐Portage
Fort W
ayne
Billings
Johnstown
Davenport‐M
oline‐Rock Island
Gainesville
Erie
Beaumont‐Port Arthur
Peoria
Chico
Norw
ich‐New London
Duluth
Spokane
Lynchburg
Trenton‐Ewing
Pueblo
Green
Bay
Topeka
La Crosse
Wausau
Boulder
Ann Arbor
Durham
‐Chapel Hill
Huntington‐Ashland
Holland‐Grand Haven
Bingham
ton
Vineland‐M
illville‐Bridgeton
Evansville
Gulfport‐Biloxi
Cham
paign
‐Urbana
Tuscaloosa
Bremerton‐Silverdale
Fayetteville
Janesville
Charleston
Yakima
Santa Rosa‐Petaluma
Lafayette
Saginaw
‐Saginaw
Township North
Springfield
Johnson City
Jackson
Bloomington
Columbus
Waterloo‐Ced
ar Falls
Racine
Bloomington‐Norm
al
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐40%
‐20%
0%
20%
40%
60%
80%
ntage Chan
ge in
Population
Cities with Smallest Percentage Change in City Population Without Excessive Friction Differences
‐100%
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
Knoxville
Green
sboro‐High Point
Bakersfield
Bellingham
Bangor
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Des Moines‐W
est Des Moines
Ren
o‐Sparks
Toledo
Wichita
Dayton
Tallahassee
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Youngstown‐W
arren‐Boardman
El Paso
Mobile
Syracuse
Winston‐Salem
Burlington‐South Burlington
Harrisburg‐Carlisle
Naples‐Marco Island
Salinas
Baton Rouge
Fort Collins‐Loveland
Hickory‐Len
oir‐M
organton
York‐Hanover
Flint
Eugene‐Springfield
Huntsville
Visalia‐Porterville
Augusta‐Richmond County
Santa Cruz‐Watsonville
Eau Claire
Amarillo
South Ben
d‐M
ishaw
aka
Joplin
Greeley
Lubbock
Corpus Christi
Salt Lake City
Rockford
Appleton
Brownsville‐Harlingen
Ced
ar Rapids
Lansing‐East Lansing
Laredo
Punta Gorda
Scranton‐W
ilkes‐Barre
Utica‐Rome
Kalam
azoo‐Portage
Fort W
ayne
Billings
Johnstown
Davenport‐M
oline‐Rock Island
Gainesville
Erie
Beaumont‐Port Arthur
Peoria
Chico
Norw
ich‐New London
Duluth
Spokane
Lynchburg
Trenton‐Ewing
Pueblo
Green
Bay
Topeka
La Crosse
Wausau
Boulder
Ann Arbor
Durham
‐Chapel Hill
Huntington‐Ashland
Holland‐Grand Haven
Bingham
ton
Vineland‐M
illville‐Bridgeton
Evansville
Gulfport‐Biloxi
Cham
paign
‐Urbana
Tuscaloosa
Bremerton‐Silverdale
Fayetteville
Janesville
Charleston
Yakima
Santa Rosa‐Petaluma
Lafayette
Saginaw
‐Saginaw
Township North
Springfield
Johnson City
Jackson
Bloomington
Columbus
Waterloo‐Ced
ar Falls
Racine
Bloomington‐Norm
al
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐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
nia Beach‐Norfolk‐…
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
Cities with Smallest Percentage Change in City Population Without Excessive Friction Differences
‐100%
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
Knoxville
Green
sboro‐High Point
Bakersfield
Bellingham
Bangor
Colorado Springs
Bridgeport‐Stamford‐Norw
alk
Seattle‐Tacoma‐Bellevue
Pensacola‐Ferry Pass‐Brent
Des Moines‐W
est Des Moines
Ren
o‐Sparks
Toledo
Wichita
Dayton
Tallahassee
Lexington‐Fayette
Fayetteville‐Springdale‐Rogers
Youngstown‐W
arren‐Boardman
El Paso
Mobile
Syracuse
Winston‐Salem
Burlington‐South Burlington
Harrisburg‐Carlisle
Naples‐Marco Island
Salinas
Baton Rouge
Fort Collins‐Loveland
Hickory‐Len
oir‐M
organton
York‐Hanover
Flint
Eugene‐Springfield
Huntsville
Visalia‐Porterville
Augusta‐Richmond County
Santa Cruz‐Watsonville
Eau Claire
Amarillo
South Ben
d‐M
ishaw
aka
Joplin
Greeley
Lubbock
Corpus Christi
Salt Lake City
Rockford
Appleton
Brownsville‐Harlingen
Ced
ar Rapids
Lansing‐East Lansing
Laredo
Punta Gorda
Scranton‐W
ilkes‐Barre
Utica‐Rome
Kalam
azoo‐Portage
Fort W
ayne
Billings
Johnstown
Davenport‐M
oline‐Rock Island
Gainesville
Erie
Beaumont‐Port Arthur
Peoria
Chico
Norw
ich‐New London
Duluth
Spokane
Lynchburg
Trenton‐Ewing
Pueblo
Green
Bay
Topeka
La Crosse
Wausau
Boulder
Ann Arbor
Durham
‐Chapel Hill
Huntington‐Ashland
Holland‐Grand Haven
Bingham
ton
Vineland‐M
illville‐Bridgeton
Evansville
Gulfport‐Biloxi
Cham
paign
‐Urbana
Tuscaloosa
Bremerton‐Silverdale
Fayetteville
Janesville
Charleston
Yakima
Santa Rosa‐Petaluma
Lafayette
Saginaw
‐Saginaw
Township North
Springfield
Johnson City
Jackson
Bloomington
Columbus
Waterloo‐Ced
ar Falls
Racine
Bloomington‐Norm
al
Percentage
Chan
ge in
Population
Cities with Largest Percentage Change in City Population Without Excessive Friction Differences
‐100%
‐80%
‐60%
‐40%
‐20%
0%
20%
40%
60%
80%
Anderson
Jacksonville
Niles‐Ben
ton Harbor
Napa
Iowa City
Hagerstown‐M
artinsburg
Los Angeles‐Long …
New York‐Northern New …
Riverside‐San
…Phoenix‐M
esa‐Scottsdale
Chicago‐Naperville‐Joliet
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
McAllen‐Edinburg‐M
ission
Orlando‐Kissimmee
Denver‐Aurora‐Broomfield
Sacram
ento‐Arden
‐ …San Antonio
Kansas City
Columbus
San Diego
‐Carlsbad
‐San
…Portland‐Vancouver‐…
Las Vegas‐Paradise
St. Louis
Jacksonville
Pittsburgh
Muskegon‐Norton Shores
Cincinnati‐Middletown
Medford
Austin‐Round Rock
Oxnard‐Thousand Oaks‐…
Cape Coral‐Fort M
yers
Santa Fe
Reading
Modesto
San Luis Obispo‐Paso …
Indianapolis‐Carmel
Raleigh
‐Cary
Cleveland‐Elyria‐Mentor
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
Allentown‐Bethlehem
‐ …Milw
aukee‐W
aukesha‐…
Tucson
Savannah
Birmingham
‐Hoover
Springfield
Richmond
Stockton
Ogden
‐Clearfield
Albany‐Schenectady‐Troy
Palm Bay‐M
elbourne‐ …
Hartford‐W
est Hartford‐…
Albuquerque
Lancaster
Grand Rapids‐Wyoming
Fresno
Buffalo‐Niagara Falls
Madison
Rochester
Akron
Columbia
Tulsa
Fargo
Deltona‐Daytona Beach‐ …
Roanoke
Omaha‐Council Bluffs
Canton‐M
assillon
Honolulu
Percentage
Chan
ge in
Population
Cities with Smallest Percentage Change in City Population Without Excessive Friction Differences
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)
Counterfactual Utility = 10.0644, Reallocation = 0.18491
ActualAvg. Efficiency
6 8 10 12 14 16 18 20-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> p
opul
atio
n)
Counterfactual Utility = 10.4243, Reallocation = 0.41605
ActualAvg. Amenities
0 5 10 15 20-6
-5
-4
-3
-2
-1
0
ln(population)
ln(p
rob
> p
opul
atio
n)
Counterfactual Utility = 11.3578, Reallocation = 0.80285
ActualAvg. Exc. Frictions
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
Correlation P-value Expected Sign
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
Correlation P-value Expected Sign
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)
Data City Characteristics
Name Pop GDP Cons Cap Hours lnAi ln γi ln gi(’000s) (m$) (m$) (m$) (Annual)
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
62
Table B.4: Data and Estimated City Characteristics (cont’d)
Data City Characteristics
Name Pop GDP Cons Cap Hours lnAi ln γi ln gi(’000s) (m$) (m$) (m$) (Annual)
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
63
Table B.4: Data and Estimated City Characteristics (cont’d)
Data City Characteristics
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
64