Geographic Fragmentation in a Knowledge Economy:
Theory and Evidence from the United States∗
Yang Jiao†and Lin Tian‡
This Version: December 2020

Abstract
We study how the rise in cross-city joint productions (or “geographic fragmentation”)—
facilitated by advancements in communication technologies—shapes the spatial skill
distribution in the United States. Motivated by observations that large cities became
disproportionately skill intensive and that industries more likely to fragment underwent
greater increases in spatial skill dispersion between 1980 and 2013, we propose a spatial
equilibrium model with cross-city production and heterogeneous skills to study how
geographic fragmentation affects spatial skill distribution. In addition to delivering theobserved facts, the model predicts that reductions in bilateral communication frictions
increase skill shares in large cities and reduce them in smaller ones. Through a novel
instrumental variable approach, we provide empirical validation of the model’s prediction. We then use the model to explore the quantitative consequences of counterfactualchanges in internet qualities on skill redistribution and real wages.

∗

We are indebted to Treb Allen, Costas Arkolakis, Davin Chor, Donald Davis, Jonathan Dingel, Jonathan
Eaton, Fabian Eckert, Pablo Fajgelbaum, Teresa Fort, Juan Carlos Hallak, Jefferey Lin, Dan Lu, Rocco Macchiavello, Andrew H. McCallum, Antonio Miscio, David Nagy, Stephen Redding, Stephanie Schmitt-Grohé,
Bob Staiger, Martín Uribe, Eric Verhoogen, Jonathan Vogel, Shang-Jin Wei, David Weinstein, and Daniel
Xu; seminar participants at Columbia, Fudan, Dartmouth, Hitotsubashi, National University of Singapore,
Drexel, Renmin and Tsinghua; and attendees at the Singapore Management University Urban Conference,
Econometric Society China Meeting, SUFE-IESR Joint Trade Workshop, and Urban Economic Association
Meeting for helpful discussions and comments at various stages of this paper. We thank Shuting Zhang
for excellent research assistance. Part of the work was done when Yang Jiao was a postdoctoral fellow at
Dartmouth College, whose hospitality is greatly appreciated.
†
FISF, Fudan University. Email: yangjiao@fudan.edu.cn‡
INSEAD & CEPR. Email: lin.tian@insead.edu

1Introduction

One of the most revolutionary developments in technology in recent decades is the rapid risein advanced communication technologies, especially with respect to internet connectivity. In
the United States, reported internet usage has increased from nonexistent in the 1980s toabout 60% in 2000, and 80% in 2013 (see the left panel of Figure 1). In particular, the fast
adoption of the Internet in the workplace—from less than 10% in 1995 to 25% in 2013, asshown in the right panel of Figure 1—alters what teams of economic agents can do at a
distance and triggers fundamental changes to the spatial organization of production. By reducing coordination frictions, the proliferation of the internet allows more cross-region teams
to be formed and leads to increasingly fragmented production processes across geographic
boundaries, both internationally and domestically. While there is an extensive literature on
geographic fragmentation across international borders by means of offshoring or international
outsourcing (see, e.g., Hummels, Ishii and Yi, 2001; Antràs, Garicano and Rossi-Hansberg,
2006; Grossman and Rossi-Hansberg, 2008), we know relatively little about domestic production fragmentation and its impacts on the labor market.
160
140

30

Internet users/100 people
Fixed broadband subscriptions/100 people
Mobile cellular subscriptions/100 people

Internet Use at Work/100 People

25
120
100

20

80
15

60
40

10
20
0
1980

1990

2000

5
1995

2010

2000

2005

2010

2015

Figure 1: Increase in Internet Usage 1980 to 2013
Data source: left panel: World Development Indicators; right panel: authors’ calculation from the Current
Population Survey Internet and Computer Use Supplement

This paper studies the economic impacts of domestic production fragmentation. Relative
to the international context, domestic production fragmentation is quantitatively important.
For example, according to a survey by the Boston Consulting Group, more than 95% of2

outsourcing, which is a prominent channel of production fragmentation, is being performed
domestically.1 Moreover, the economic implications generated by increasing domestic production fragmentation are distinctively different from those performed internationally. The
key difference between these forms of production fragmentation is the assumption of labormobility. Individuals are generally assumed to be immobile across international borders,
whereas they are relatively mobile, especially in the long run, across cities within a country.
Given this, as different economic activities move across city boundaries due to production
fragmentation, relative local demand for different skills also changes. Domestic fragmentationof production may therefore lead to a redistribution of skills across local labor markets andgenerate very different implications for welfare, productivity, and wage inequalities, both at
the aggregate level and their corresponding spatial distributions across cities, in contrast to
the international context.
In this paper, we develop a theoretical framework and present empirical evidence showing
how the formation of cross-region production teams—facilitated by improvements in communication technologies in general and the Internet in particular—shapes the spatial distributionof skills domestically across U.S. cities. The production of goods involves two distinct setsof inputs: more skill-intensive knowledge inputs and relatively less skill-intensive standardized production (Garicano and Rossi-Hansberg, 2006; Arkolakis et al., 2018). Larger cities
have a comparative advantage in the more skill-intensive tasks (Davis and Dingel, 2019), andtherefore attract a greater share of high-skill workers who specialize in knowledge production.
Workers performing tasks related to standardized production, on the other hand, tend to locate in smaller cities to save on costs. Cross-city production teams—with high-skill workers
in larger cities and low-skill ones in smaller cities—allow workers to take advantage of thedifferentiated locational benefits offered in cities of different sizes. Declining communication
costs render such production arrangements more viable, which reinforces the initial patternof specialization across cities.2 As a result, larger cities become even more specialized inskill-intensive tasks, thus driving up the share of skilled workers in these locations.
Motivated by these insights, we first assemble a set of stylized facts that connect the observed spatial skill redistribution with the trend of rising production fragmentation across
U.S. cities. Using commuting zones to define cities, we show that larger cities specialize inskill-intensive activities. Importantly, this pattern of specialization became more pronounced
between 1980 and 2013, as high- and low-skill workers were increasingly segregated spatially.
1

Source: BCG Global Outsourcing Survey, 2015.
https://mkt-bcg-com-public-images.s3.
amazonaws.com/public-pdfs/legacy-documents/file14496.pdf.
2
In this paper, we do not distinguish between "firms" and "production teams" , while allowing for collaborations in production to happen both intra- and inter-firms. For example, a furniture production team canbe either an individual firm or consist of two firms: a furniture design firm and a furniture factory.

3

To connect this observed trend of spatial segregation with our proposed mechanism of production fragmentation, we show that the observed industry-level extent of spatial segregationis stronger for industries with a greater tendency to fragment their production processes.
We then develop a theoretical framework that delivers the observed spatial skill segregation. We propose a spatial equilibrium model in a system-of-cities setting, with fragmentation
costs—e.g., the costs of communicating and coordinating when the economic agents who specialize in different tasks are not located in the same geographic area. There are two typesof agents: high-skill workers, who produce knowledge about or the “blueprint” of a product,
and low-skill workers, who engage in the actual production. Agents are mobile across space.
High-skill workers choose the spatial organization of production—i.e., within-city or crosscity production teams—as well as the production location and scale to maximize profits.
Equilibrium conditions determine the extent of production fragmentation and the distribution of skills, wages, and housing prices across cities. Furthermore, the model also generates
testable predictions regarding the impact of communication cost reduction on spatial skill
distribution. In particular, it would increase the share of high-skill workers in larger cities
and reduce it in smaller ones.
We next provide empirical support for the model prediction by examining the impact
of internet improvement on the skill composition within cities. To overcome the identification difficulty associated with the endogeneity of local internet quality, we adopt a novel
instrumentation strategy inspired by the literature that uses geological features as a meansof identification (e.g., Juhasz and Steinwender, 2018). Specifically, we leverage the uniquefeatures of U.S. broadband technology and instrument the quality of Internet connectivity
using elevation levels of the local terrain. The analysis yields causal evidence that validates
our main theoretical prediction.
Finally, we parameterize our model to examine the quantitative consequences of domestic
geographic fragmentation. For the quantitative exercise, we assemble a unique data set thatcombines census data, internet bandwidth records, and the Orbis Database, which reports
direct shareholder information for subsidiary plants. The Orbis data allow us to directly
measure the extent of one specific form of cross-city joint production: the headquarterssubsidiary relationship. Using this data set, we compute the bilateral fragmentation costs
between city pairs and estimate the core structural parameters, which include the elasticity offragmentation with respect to internet quality. We conduct counterfactual analyses to evaluate how internet improvement affects spatial skill redistribution and the real wages of highand low-skill workers, both directly and indirectly, through general equilibrium reallocation.
In one exercise, we simulate a counterfactual scenario in which there is no internet improve4

ment since the 1980s. We show that the extent of spatial skill redistribution would have been
about 60% lower, which demonstrates the quantitative importance of our proposed mechanism. Regarding welfare, unsurprisingly, internet improvement has increased real wages forboth high- and low-skill workers. More distinctly, a substantial share of the welfare improvement is driven by spatial reorganization arising from more fragmented production acrossdifferent cities, as shown by our framework. We conduct a second counterfactual exercise
to quantitatively evaluate widely adopted programs that aim to improve internet access forunderdeveloped areas. By upgrading the internet in areas with below-median quality to themedian level, we show that more evenly distributed internet provision promotes spatial skill
divergence and increases real wages for both high- and low-skill workers.
This paper is related to several strands of the literature. First, domestic production fragmentation is driven by similar economic forces as international production fragmentation
through offshoring or outsourcing. A large volume of research studies how falling transportation or communication costs motivate firms to disintegrate production and send certain jobs overseas to take advantage of comparative advantages (see, e.g., Feenstra, 1998;
Hummels, Ishii and Yi, 2001; Antràs, Garicano and Rossi-Hansberg, 2006; Grossman andRossi-Hansberg, 2008). While the two types of production fragmentation share the sameunderlying driving forces, our work contrasts with this literature by focusing on the domestic context, thereby highlighting both the shared and divergent economic implications withrespect to labor mobility.
Our work is also closely connected to the small literature on cross-city analysis of production fragmentation. Duranton and Puga (2005) pioneer the theoretical research, for which
they develop a model with homogeneous labor that is mobile across cities and sectors. The
authors conclude that low communication cost facilitates the separation of managerial andmanufacturing units in different cities. Liao (2012) extends the canonical model to include
two types of workers and focuses specifically on business support services.3 The paper documents that low-skill support workers tend to leave large cities and migrate to rural areas,
and finds that these low-skill workers are rendered better off because firm fragmentation
allows support workers to benefit from the higher productivity in cities without bearing thehigh costs. A contemporaneous work by Eckert (2019) studies the impact of communication
cost reduction on interregional trade in business services. Through a quantitative model,
Eckert (2019) shows that trade in business services is an important force that drives boththe increase in the aggregate college wage premium and the dispersion of the growth in wage
premia across space.4 Relative to the literature, our paper is novel along several dimen3
4

Workers in the business support services sector account for less than 1% of total employment in the U.S.
Relatedly, Eckert, Ganapati and Walsh (2020) show that the rise of several skilled tradable service

5sions. First, we document new facts that link an industry characteristic—the propensity offragmentation—to the observed pattern of spatial skill redistribution. Second, we go beyond
the role of country-level communication technologies improvement and study the heterogeneous effects of internet improvement across cities of different sizes, both theoretically andempirically. Finally, we develop and estimate a spatial equilibrium model with heterogeneous
workers to quantify the role of internet infrastructure in shaping the skill distribution of the
U.S. labor market.
A large empirical literature supports our theoretical framework and results. Manufacturers often contract out specialized business services (Abraham and Taylor, 1996; Aarland
et al., 2007), and this propensity increases with city size (Ono, 2007). In particular, thosewith headquarters in large cities are more likely to contract out less important parts of the
production process (Ono, 2003). An important determinant of firms’ decision to geographically separate the headquarters from production is the proximity to production facilities(Holmes and Stevens, 2004; Henderson and Ono, 2008). In addition, this spatial specialization pattern has become more pronounced over time. Strauss-Kahn and Vives (2009) showthat between 1996 and 2001, headquarters tend to move away from locations with relatively
few other headquarters and business services producers, and toward locations with more of
both. Duranton and Puga (2005) document the pattern of increasing functional specialization in U.S. cities through time, with larger cities more specialized in management functions
and smaller cities in production. Our model is able to reproduce all of these empirical results.
Our paper is among the growing literature that develops models of a system of cities.
Davis and Dingel (2019) incorporate Costinot and Vogel (2010) in a city system with explicit
internal urban structures. They show that larger cities are skill-abundant and specialize inskill-intensive industries. Although agglomeration force is exogenously given in that paper,
Davis and Dingel (2012) endogenize this human capital externality based on idea exchange.
Our paper does not address the source of agglomeration explicitly, but we argue that humancapital externality between high-skill workers who engage in more cognitive tasks is a natural
assumption, and possibly arises from the force described in Davis and Dingel (2012) orDuranton and Puga (2004). Behrens, Duranton and Robert-Nicoud (2014) also use a modelwith a system of cities. Whereas all of the papers above construct models with a systemof cities, we study the endogenous choice of cross-city production teams with heterogeneous
agents, with an explicit emphasis on production organization. That is, cross-city organization
is a specific form of linkage between cities we would like to highlight.
Finally, our paper is closely related to the literature on quantitative spatial equilibrium
industries that use ICT intensively is important to the understanding of the rising inequality in U.S.

6

analysis, e.g., Allen and Arkolakis (2014) and Allen, Arkolakis and Takahashi (2020). Previous literature mostly focuses on transportation infrastructure, which affects trade cost. We
differ by considering communication technology infrastructure, and the internet in particular. In our framework, internet improvement affects cross-city joint production cost insteadof transportation cost. By doing so, our paper connects with a body of literature that studies the effect of modern technology improvement on production organization (see, e.g., Fort,
2017; Tian, 2019).
The rest of the paper is organized as follows. Section 2 presents the empirical findings.
Section 3 and Section 4 introduce the model, provide theoretical analysis, and derive equilibrium properties. Section 5 investigates the heterogeneous effects of internet improvement on
skill composition across cities of different sizes. Section 6 provides a quantitative evaluationof our model and presents results from the counterfactual exercise. Section 7 concludes.

2

Data and Stylized Facts

In this section, we empirically study the relationship between spatial skill redistribution
and the trend of rising production fragmentation using data on U.S. cities. We begin bydescribing and defining variables. Using the data set, we establish three stylized facts: (1)larger cities specialize in skill-intensive activities; (2) between 1980 and 2013, there had beena substantial increase in the extent of spatial segregation of skills across U.S. cities; and (3)this trend of increasing spatial skill segregation is more concentrated in industries with agreater propensity to fragment their production processes. Together, the stylized facts form
the empirical foundation for the ensuing theoretical framework.

2.1

Data Description

Our analysis mainly draws on the Integrated Public Use Micro Samples (IPUMS, Ruggles
et al., 2015). For 1980, we use 5% Census samples; for later years, we combine the 2011, 2012,
and 2013 1% American Community Survey (ACS) samples. Our worker sample consists ofindividuals who were between the ages 16 and 64 and who were working in the year preceding the survey. Residents of institutional group quarters, such as prisons and psychiatricinstitutions, are dropped along with unpaid family workers.
We define a city as a commuting zone (CZ), which is the geographic unit of analysis
developed by Tolbert and Sizer (1996) and applied in a number of papers, including Autor

7and Dorn (2013) and Burstein et al. (2020). Each CZ is a cluster of counties characterized
by strong commuting ties within and weak commuting ties across zones. For our analysis, we
include 722 CZs in the continental U.S. We measure city size using the log of labor supply,
which is measured by the product of weeks worked times the usual number of hours worked
per week.5 All calculations are weighted by the Census sampling weight multiplied by thelabor supply weight.
Throughout the paper, we classify workers into high- and low-skill groups using theiroccupation wage in 1980. Following Acemoglu and Autor (2011), we rank the skill levelsof different occupations, approximated by the mean log hourly wage of workers in each
occupation in 1980.6 We define high-skill workers as those whose occupation wage rank ishigher than 75% of occupations in 1980. We vary the cutoff in robustness checks to 67%
and 80%. Further robustness checks using education information to classify the high andlow skilled, with the high skilled defined as those with a college education or above, are also
provided in the Appendix.
The empirical analysis in Section 5 uses internet quality data drawn from the U.S. Federal
Communications Commission (FCC) Fixed Broadband Deployment Database. Fixed broadband providers are required to provide the lists of census blocks in which they offer service
in at least one location within the block. The database is available from December 2014
and also provides additional information about the quality of the service, including download and upload bandwidths (reported in megabytes per second). We identify the maximum
bandwidth at the block level and compute the population-weighted internet quality at the
CZ level.7
Finally, in the quantitative exercise in Section 6, we measure the extent of firm fragmentation using the Orbis Database for 2018 from Bureau van Dijk, which reports direct
shareholder information for subsidiary plants. We define a headquarters-subsidiary pair if
a headquarters has strictly more than 50% of the ownership of a given subsidiary. Using
location information, we construct a CZ-pair-level fragmentation measure that counts the5

We use labor supply instead of number of workers to measure city population to be consistent with ouruse of hourly wage. The stylized facts are robust when we use number of workers, and are available uponrequest.
6
Examples of occupations in the lower, middle, and upper wage-rank distributions are child-care workers,
waiters and waitresses, housekeepers, and hotel clerks; machine operators, reception and information desk,typists, and carpenters; CEOs, engineers, architects, financial managers, and software developers, respectively.
7
The 15-digit census block ID comes from the 2010 census. In computing the population-weighted average internet quality measures, we use the 2010 population information at the PUMA level—the smallest
geographic unit in the 2010 Census. We aggregate data from the more finely divided census block level tothe PUMA level using simple averages.

8

number of headquarters-subsidiary pairs for a given pair of CZs.

2.2

Stylized Facts on Skill Distribution

Using the IPUMS data set, we document patterns of spatial skill redistribution across U.S.
cities and investigate how the spatial pattern is related to domestic production fragmentation.

6

8

10
12
city size
1980

14

.01

-.05

0

skilled share.05

change in skilled share 1980-2013
.02
.03

.04

.1

The left panel of Figure 2 depicts a well-known fact: The largest cities, measured by thelabor supply, are the ones that have the highest shares of high-skill employment in both 1980
and 2013. This pattern of skill specialization suggests comparative advantage differences
across cities of different sizes: Larger cities have a comparative advantage in more skillintensive activities, possibly due to stronger agglomeration forces, and smaller cities have acomparative advantage in less skill-intensive activities, aided by the lower labor costs.

16

6

2013

8

10
12
city size

14

16

Figure 2: Change in High-skill Employment Share with Respect to City Sizes
Notes: The left panel displays the regression line for the high-skill share (demeaned) in 1980 and 2013 against
log of 1980 labor supply. The right panel displays the change in the skilled share from 1980 to 2013. Highskill is defined as occupation rank above 75% using the 1980 mean of log hourly wage.

Moreover, this pattern of specialization became more pronounced over time. The rightpanel of Figure 2 plots the change in the skilled share within a city between 1980 and 2013
against the corresponding city size in 1980.8 It shows that larger cities experienced a greater
8

Figure 10 in the Appendix provides the scatter plot for the raw data.

9

increase in the share of high-skill employment between 1980 and 2013, thereby becoming
even more skill intensive. For example, the share of high-skill employment in the largest
city in the U.S. had risen by 4 percentage points, whereas it only increased by less than 1
percentage point in the bottom percentile of the city-size distribution. Table 1 reports theformal statistical test, in which we regress changes in the share of high-skill employment at
the city level onto the city sizes measured by the log of 1980 city-level labor supply. We findstrong positive correlation between city size and magnitude of the change in the high-skill
employment share.9
Dependent variable:

City Size
State fixed effectObservations
R2

Change in high-skill employment share
1980-2013(1)(2)
0.0036∗∗∗0.0050∗∗∗(0.001)(0.001)
No
Yes
722
722
0.037
0.357

∗ p < 0.10, ∗∗ p < 0.05, ∗ ∗ ∗ p < 0.01

Table 1: Change in High-skill Employment Share and City Size
Notes: City size is measured by the log of total labor supply in 1980 within a commuting zone. High-skill
workers are defined as workers whose occupation wage rank is higher than 75% of occupations in 1980.
Column (1) reports results using robust standard errors, and Column (2) reports results with standard
errors clustered by state.

The spatial redistribution of skills, established in the previous set of results, suggests anincrease in the spatial segregation of high- and low-skill workers over the period between 1980
and 2010. To study this spatial segregation more directly, we adopt a variant of the Kremer
and Maskin (1996) measure of the degree of segregation, i.e.,
1X
ρ=
S s

"P

2
c Ncs · (πcs − πs )Ns · πs · (1 − πs )#,where s ∈ {1, 2, . . . , S} denotes a sector as defined by Census ind1990 codes, Ncs is the
skilledemployment in sector s and city c, Ns is the total sectoral employment, πcs = NcsNcs isskilledthe high-skill employment share in sector s and city c, and πs = NsNs
9is the high-skill

Table 14 in the Appendix reports robustness checks regarding the definition of the high skilled using a
67% occupation wage rank cutoff and an 80% occupation wage rank cutoff, as well as an analysis that uses
education to separate high- and low-skill workers.

10

employment share in sector s.10 As shown in Table 2, the Kremer and Maskin (KM) index,
denoted by ρ, almost tripled from 1980 to 2013, indicating that the high skilled and low
skilled had become increasingly more spatially segregated.
Yearρ

95% Confidence Interval

1980
2013

0.007460.0204(0.00741, 0.00752)(0.0202, 0.0205)

Table 2: KM Segregation Index in 1980 and 2013
Notes: High-skill workers are defined as workers whose occupation wage rank is higher than 75% ofoccupations in 1980. The 95% confidence interval of the index of segregation is:
F (N − J, J − 1)0.025
F (N − J, J − 1)0.975,
1−ρ ≤ ρ̃ ≤F (N − J, J − 1)0.025 + ρ
F (N − J, J − 1)0.975 + 1−ρρwhere J = C + S (Kremer and Maskin, 1996).

The combined evidence from the two analyses above suggests that there has been growing
spatial segregation of high- and low-skill workers, with larger cities increasingly specializingin high-skill occupations and smaller cities in low-skill occupations.
Next, we link the observed increase in spatial segregation with our proposed mechanismof increasing production fragmentation across U.S. cities. In particular, we show that thispattern of segregation across space at the industry level is closely related to production
fragmentation activities in the U.S. economy. Fort (2017) documents that firms’ adoption ofcommunications technology facilitates their sourcing, particularly from domestic suppliers.
If the observed segregation is linked to greater sourcing of tasks, one would expect thatindustries experiencing more sourcing would also undergo greater skill segregation. Figure
3 confirms this hypothesis by illustrating the relationship between the change in the KM
index and the fraction of plants that engage in sourcing activities. These are measured
by the purchases of contract manufacturing services (CMS) from other plants (within its
own company or from another company) in each of the 86 four-digit NAICS manufacturing
10

This index measures how correlated the employment shares of different occupations are within a citysector. It is constructed as the ratio of the variance of share of the high-skill across cities to the variance of anagent’s occupation status (i.e. the high skilled vs. the low skilled) of the a given sector, which is equivalent to
the R2 value of a regression of the share of high skilled on a series of city dummies. When ρ = 0, there is nosegregation; i.e. the high skilled and low skilled are always in the same cities; when ρ = 1, there is complete
spatial segregation of the high skilled and low skilled. We calculate the national average as an average value
across sectors to account for possible changes in industry composition within cities across time.

11

0

.5

1

1.5

2

industries.11 For example, the computers and related equipment industry, which has a very
high sourcing index (50% of plants source from another plant), features a relatively large
increase in the KM index; in contrast, the bakery product industry has a very low sourcing
index (8% of plants source from another plant) exhibits a slight decrease in the KM index.

0

.2
.4
Fort (2017) Firm Sourcing Index
95% CI
Change in KM Segregation Index.6
Fitted values

Figure 3: Change in KM Skill Segregation Index and Fragmentation Index Across Sectors
Notes: Each point denotes an industry. The shaded area displays the 95% confidence band around thepoint estimates for the slope. The correlation between change in KM skill segregation index and Fort(2017) sourcing index is 0.47.

In summary, we establish that larger cities have a comparative advantage in skill-intensive
activities (Fact 1). This pattern of specialization became stronger over the past three decades,
as high- and low-skill workers become more segregated geographically (Fact 2). The extent ofsegregation varies across industries systematically, matching the cross-industry heterogeneity
in the extent of production fragmentation (Fact 3). These three facts form the empirical basis
for our central hypothesis: Improvements in internet technology over the last three decades
allowed firms to better leverage comparative advantage differences across cities by engaging incross-city production, which allows them to locate different segments of production activities
in different geographic regions. This reinforces the initial pattern of specialization and drives
11

Fort (2017) provides this measure at the four-digit NAICS level. We employ the industry code crosswalk
between census industries and NAICS industries provided by the Census Bureau, so that each census industry
is assigned to the corresponding NAICS code. If one Census industry corresponds to multiple NAICS codes,
we calculate the simple average of the fragmentation indices among those NAICS codes as that census
industry’s fragmentation index. We are left with 67 census industries. See Table 13 in the Appendix for a
detailed list of industries and their change in KM index and Fort (2017) index.

12the redistribution of skills observed in the data. In the next section, we build on these insights
and propose a quantitative model with cross-city production teams that captures these forces
in a rich geographic setting, to study the impact of geographic production fragmentation,
enabled by communication cost reduction, on the skill distribution across cities.

3

The Model

The theory embeds a model of firms’ production organizations in a system-of-cities settingwith heterogeneous agents. The basic logic of the model can be sketched as follows: In themodel, larger cities have a comparative advantage in the relatively skill-intensive managerial
activities performed by high-skilled workers over less skill-intensive production activities performed by lower-skill workers. A reduction in cross-city collaboration costs would induce agreater extent of cross-city collaborations (or domestic fragmentation of production), resulting in larger cities specializing more in managerial activities and smaller cities in production
activities. Given spatial mobility, changes in the relative local labor demand will lead tospatial redistribution of skills, with high-skilled workers becoming increasingly concentrated
in larger cities.

3.1

Set-up

We consider an economy with a finite number of cities, indexed by n ∈ N ≡ {1, 2, . . . , N }.
There is a continuum of agents, distinguished by their exogenously-given skill levels, each ofwhom inelastically supplies one unit of labor. The measures of high-skilled workers (which
we refer to as managers) and low-skill workers (which we refer to as production workers) are
Lm and Lp , respectively.
Individuals consume two goods: a homogeneous tradable good and housing. The utility
function follows a standard Cobb-Douglas form:
U (c, h) = α−α (1 − α)−(1−α) cα h1−α ,(1)where c is the consumption of the tradable good and h is the consumption of housing. Managers and production workers choose their residential locations to maximize their utility.12
12

A number of papers study the various forms of mobility cost in reality; see, e.g., Enrico (2011), BaumSnow and Pavan (2012), and Ferreira, Gyourko and Tracy (2011). This paper focuses on long-run changes
in the labor market. We thus takes the position that in the long run, individuals are highly mobile.

13

The homogeneous tradable good is produced everywhere in the economy with varying
productivity levels, as specified below. Each production team consists of a single manager
and l homogeneous production workers.13 A manager living in city n can choose to locate
the production team in any city c ∈ N .14 Managers living in n and producing in c 6= n
incur a productivity loss that we model as iceberg bilateral fragmentation costs, τnc ≥ 1,with τnn normalized to 1. These costs reflect the costs of managing off-site workers, e.g.,communication or coordination frictions between managers and production workers locatedin different cities. Formally, a manager living in n and managing workers in c has the following
production technology:
anc β
l .
(2)
ync =
τnc
The production technology, which follows Lucas (1978), has three elements: First, anc denotes the “manager’s productivity,” which we discuss below; second, τnc reflects the iceberg
productivity loss of managing an off-site production team; and third, β < 1 is an element ofdiminishing returns to scale, or the manager’s span of control.
A manager in n is characterized by a productivity vector an = {an1 , an2 , . . . , anN }. These
productivity vectors are origin-city specific and vary across managers, causing managers inn to make different choices regarding production locations. In doing so, we assume that the
productivity heterogeneities originate from managers, who take the role of developing theblueprint for the products and providing management capital for the production process.15
The manager’s productivity, anc , has two components: (1) local agglomeration force f (Lmn ),which is an increasing function of the total mass of managers in city n, Lm
n ; and (2) a randomdraw, denoted by ānc . The two components are assumed to enter the manager’s productivity
function multiplicatively:
anc = f (Lm(3)
n )ānc .
In particular, a manager who lives in city n draws her productivity ānc from N cities simultaneously. Each ānc is drawn independently from a Fréchet distribution with a cumulative
distribution function given by
G(ā) = exp −Tn ā−θ ,where Tn is an exogenous technology parameter representing city n’s fundamentals, such as
13

Note that this production setup is equivalent to any constant returns to scale production function. Boththe high-skill input M and the low-skill input L can be equivalently translated into M production teams, eachL
production workers.
of which consists of a single manager and M
14
To the extent possible, we use n to denote the manager’s residential location (the source of the blueprint
or management capital) and c to index the location of the production.
15
It is straightforward to extend the model to allow worker productivity to vary with production locations
in such a way that none of the results that we focus on are affected.

14

natural resources endowment or geographic location, that potentially affect labor productivity. θ represents the dispersion of the draws: A higher value θ > 0 decreases the dispersionof the manager’s productivity across locations.16

3.2

Manager’s Optimization

In this environment, managers face a three-step optimization problem. First, a manager
chooses where to live, which is also where she works or where the firm’s headquarters arelocated. Second, the manager chooses her firm’s spatial production organization (i.e., locationof the production team). Finally, the manager decides on the production scale (i.e., how many
workers to hire). We consider the optimization problem in a backward order, starting fromthe last step.
3.2.1

Production Scale

Managers are the residual claimants of the firm’s profit. The income of a manager who lives
in city n and manages workers in city c is
πnc =

anc β
l − wc l,τnc(4)

where wc is the wage of workers in city c. Recall also that τnc ≥ 1 is the iceberg cost thatreflects the cost of managing workers remotely—e.g., the communication cost between cityn and city c.
Given anc , a manager chooses the size of her production team, l, to maximize her income.
Taking the first-order condition of (4) with respect to l, we obtain the optimal production
scale l∗ ,1βanc 1−βl∗ = () ,(5)
τnc wcwhere a more productive manager (higher anc ) manages a larger production team.
Combining (4) and (5), a manager living in city n with a production team in city c has
an income of:β1
anc 1−β∗πnc= β 1−β (1 − β)().
(6)τnc wcβNote that both a higher iceberg fragmentation cost τnc and a higher worker wage wc would
16

The assumption of having i.i.d draws across all locations is observationally equivalent to a joint Fréchet
distribution assumption. See Eaton and Kortum (2002), footnote 14, for a discussion.

15

reduce the manager’s income.
3.2.2

Production Locations

A manager who lives in city n chooses to locate the production team in a city that max∗
imizes her income πnc, as specified in (6). The Fréchet assumption on the idiosyncraticcomponent of manager’s productivity allows us to derive the following result, which we callthe fragmentation gravity equation.
Proposition 1 The probability of a manager who lives in city n and locates production incity c isTn (τnc wcβ )−θ
,
Φn

(7)

where Φn , city n’s “fragmentation potential”, is defined byΦn ≡XTn (τnk wkβ )−θ ,

(8)

k

where

P

n∈N Φn = 1.

Proof. See Appendix A.
Based on this proposition, it is easy to see that an internet infrastructure developmentthat drives down cross-city fragmentation cost, τnc , increases the possibility of cross-city
production teams relative to domestic production teams, all else equal. By the Weak Law ofLarge Numbers, the above gravity equation also gives the share of managers living in city nand locating their production teams in city c:
xnc ≡

3.2.3

Tn (τnc wcβ )−θ
Lm
nc
=
.
Lm
Φn
n

(9)

Residential Locations

Individuals choose their residential location to maximize utility. From (1), we derive theindirect utility function for an agent with income πn facing rent pn in city n:
V (pn , πn ) =

16

πn
.
p1−α
n

(10)

Additionally, given the Cobb-Douglas preference, the equilibrium housing rent in city n isgiven by(1 − α)Wn
,
(11)
pn =
Hn
where Wn is the total income in city n, including both city n managers’ and production
workers’ income, and Hn is the exogenously given housing supply in city n.
∗in (6), we canGiven the distribution of the productivity draws and the profit function πnc
derive the distribution for managers’ income.

Proposition 2 The income of a manager who lives in city n follows the following Fréchet
distribution with a cumulative distribution function:θ−θ(1−β)G(π) = exp −[β −β (1 − β)−(1−β) ]−θ (f (Lm.
n )) Φn π(12)

Proof. See Appendix A.
By the properties of a Fréchet distribution, the expected income of a manager living incity n is thus1θθ(1−β) ,E[πn ] = ζ[[f (Lm(13)
n )] Φn ]βwhere ζ ≡ θβ 1−β (1 − β)2 0+∞ exp −x−θ(1−β) x−θ(1−β) dx.
R

Managers choose their residential locations to maximize their indirect utility in (10).
Denoted by Ψn , a manager’s natural logarithm of the expected utility function is given by
E[πn ]
Ψn = logp1−αn!

= const +1
1
log[f (Lmlog Φn − (1 − α) log pn .
n )] +1−β
θ(1 − β)(14)

A manager’s problem is therefore to maximize Ψn . In equilibrium, managers are indifferent
between living in city n and n0 (conditional on there being non-zero managers in both cities),
so that Ψn = Ψn0 , ∀n, n0 ∈ N , or1
1log[f (Lmlog Φn − (1 − α) log pnn )] +1−β
θ(1 − β)1
1=log[f (Lmlog Φn0 − (1 − α) log pn0 .
n0 )] +1−β
θ(1 − β)

17

(15)

3.3

Worker’s Optimization

Similar to managers, production workers also choose the city they live in to maximize their
indirect utility in (10), given their income wn and housing price pn . In equilibrium, production
workers are indifferent and thus receive the same indirect utility across cities, i.e., Vnw = Vnw0 =v̄ ∀ n, n0 ∈ N . We therefore obtain the following equilibrium condition:
wn /pn1−α = wn0 /pn1−α
.
0

4

(16)

Equilibrium Analysis

In this section, we characterize the spatial equilibrium. We first define spatial equilibrium,then provide more intuition by considering a special “fragmentation autarky” case, in which
the fragmentation cost is infinite. We next focus on a simplified two-city model to derive
analytic results for the effects of changes in fragmentation costs, τnc , on the distribution ofskills. We finally perform numerical simulation in a multi-city scenario.

4.1

Definition

In a spatial equilibrium, managers and workers are indifferent across locations.17 With exogenous parameters {Tn , τnc , Hn }, ∀n, c ∈ N and a mass of managers LM and workers LP ,P
an equilibrium is a vector of labor allocations {Lmnc , Lnc } and prices {pn , wn } such that:
1. Production workers maximize their utility in (10);
2. Housing prices pn are determined by (11);3. Managers maximize their expected utility in (14);4. Labor markets clear for both managers and workers:
Lm =

X

Lm
n =

n

Lm
nc ,

(17)

Lpnc ,

(18)

X
n,c

and
Lp =

X

Lpn =

n
17

X
n,c

Given the unbounded Frechét distribution draws, we can show that all cities have a nonzero mass of
production workers. Additionally, to be consistent with the data, we further assume that city fundamentals
ensure that all cities have a nonzero mass of managers.

18

where Lpnc refers to the mass of production workers hired by managers from n and living
in city c. This is given by

1

Lpnc = ηwc−1 Tn (τnc wcβ )−θ Φnθ(1−β)
1where η = β 1−β−1

11−β Lm ,[f (Lm
n )]
n

(19)

R∞ − 1y θ(1−β) e−y dy.18
0

In Appendix C, we provide further details on the equilibrium characterization. Further,
we show, using Banach fixed point theorem, a set of sufficient conditions under which theequilibrium exists and is unique.

4.2

Equilibrium with Infinite Fragmentation Cost

For the subsequent derivation of analytical results, we adopt a functional form assumption
for the agglomeration force,
m γ
f (Lm
n ) = (Ln ) ,where the γ ≥ 0 parameter governs the extent of agglomeration externalities.
We first consider a special “fragmentation autarky” case, in which the bilateral fragmentation cost τnc → +∞, ∀n 6= c. In this scenario, the system of equilibrium conditions reads
as follows:
1
1
m
θ
θ
(20)
γ(log Lmn − log Ln0 ) = (log wn − log wn0 ) − (log Tn − log Tn0 )
and
!

1
β
+
(log wn −log wn0 ) =1−α 1−β

!

1
1
γ
1
m
+ 1 [log Lm[log Tnθ −log Tnθ0 ].
n −log Ln0 ]+
1−β
1−β
(21)

In this case, the cross-city fragmentation cost is prohibitively high, such that all managers
will hire production workers in the same city as the one in which the manager lives. Weγ
can show that under regularity conditions—i.e., γ + 1 > 1−α—cities with high technology
parameters (Tn ) not only have a larger fraction of the whole population, but also have alarger fraction of both the high-skilled population and the low-skilled population.19 More18

See Appendix D for details on derivation of the demand for production workers.
γ
The assumption that γ + 1 > 1−αimplies that the elasticity of agglomeration, which is positively
correlated with γ, is smaller than the elasticity of urban costs, which is positively correlated with 1 − α. This
ensures that cities have a finite size in equilibrium. See Behrens, Duranton and Robert-Nicoud (2014) for an
excellent discussion.
19

19

formally, we state the results in the following proposition.
γ
m γ
Proposition 3 Given f (Lmn ) = (Ln ) and γ + 1 > 1−α , when τnc → +∞, ∀n 6= c, thespatial equilibrium exists and is unique. The number of managers in each city Lmn and thenumber of production workers in each city Lpn satisfy that

1

−1

1
θ
1−α

1−α
where κ = 1+γ−γκLmn ∝ Tn ,(22)

Lpn ∝ Tnκ ,

(23)
m

n
> 0. As a result, the high-skill employment share LmL+L
p is the samennacross all cities.
Proof. See Appendix A.

4.3

Equilibrium with Finite Fragmentation Costs

We next analyze the equilibrium with finite fragmentation costs. We start with a simple twocity case to elucidate the mechanism of skill relocation after a reduction in fragmentation
costs. We then extend the analysis to a multi-city scenario.

4.4

Two-city Analysis

We start with a two-city case with quasi-symmetric communication cost and fixed housing
supply.20 Using the simple model, we highlight the mechanism behind the skill relocation
after cross-city communication cost reduction.
First, it is easy to see that when the cross-city fragmentation cost is infinite, the city withLm
the greater technology parameter is larger and more skill intensive. We can solve for L1m and
2

w1
w2

explicitly using (20) and (21):

log

α
1
1
Lm
1−α
1
θ
θ
=
γ [log T1 − log T2 ]m
L2
γ + 1 − 1−α

(24)

20
We assume Hn = Hc = 1 in this section to highlight the role of the comparative advantage of cities intechnology Tn . The analysis can easily be extended to the case with different city-level housing supplies. In
our quantitative section, we take into account housing supply heterogeneity.

20

and
log

1
1
w1
1
θ
θ
=
γ [log T1 − log T2 ].
w2
γ + 1 − 1−α(25)Suppose, without loss of generality, that T1 > T2 . Then from (24) and (25), it is obviousthat the population in city 1 is higher than that in city 2. With a reduction in communication
cost, we can show that a small reduction in fragmentation cost—e.g., an improvement ininternet quality that facilitates cross-city communication—results in a spatial reallocation ofskills. Specifically, the share of high-skill employment in the initially larger city will increase,
whereas the share of high-skill employment in the initially smaller city will decrease.
Proposition 4 In the two-city case, if τ12 = τ21 goes down around the neighborhood of thepminfinite communication cost, and suppose that T1 > T2 , then Lm
1 and L2 would go up, L2 andLp1 would go down. A stronger agglomeration force (larger γ) implies larger labor reallocation
for both the high-skilled and the low-skilled.
Proof. See Appendix A.
This proposition states that if internet improvement reduces cross-city communication
cost, then our model is able to replicate the observed fact that bigger cities are attracting alarger proportion of the high skilled in recent decades. Through a numerical simulation of thetwo-city equilibrium, we confirm the proposition’s prediction on skill flows after the internet
improvement. As shown in the left panel of Figure 4, when the ICT openness—defined as theinverse of the fragmentation costs—increases, the share of managers increases in the larger
city, whereas the share of managers goes down in the smaller city, as shown in the right panelof Figure 4.21
We also consider the welfare implications of a reduction in communication cost. In general,simulations support the notion that both managers and workers benefit from communication
cost reduction. Intuitively, the drop in the iceberg communication cost is similar to the
productivity increase in the production function in a Hick’s neutral way. However, deriving
an analytical result for the welfare impact is hard with the spatial reorganization, because
the real wages of managers and workers are endogenous to each other.22 We provide local
analyses of agents’ welfare in Appendix B. In our quantitative analysis section, we directly
examine the welfare implications with calibrated parameters.
Formally, ICT openness, denoted by 4, is defined as τ −θ .
This is because both managers and workers consume housing, and housing prices enter into the welfare
functions of both types of agents.
21

22

21

1

0.34
0.32

0.9
Share of Managers in City 2

Share of Managers in City 1

0.3
0.8

0.7

0.6

0.5

0.28
0.26
0.24
0.22
0.2
0.18

0.4
0.16
0

0.2

0.4
0.6
ICT Openness ∆

0.8

1

0

0.2

0.4
0.6
ICT Openness ∆0.8

1

Figure 4: Two-city Equilibrium: High-skill Employment Share in City 1 and City 211

Notes: In this simulation, we set θ = 5, T1θ = 1.5, T2θ = 1.0, Lm = 1, Lp = 2, γ = 0.1, α = 0.4, β = 0.4,
H1 = H2 = 1.0. The vertical axes show the share of managers in City 1 (the larger city) in the left panel andthat in City 2 (the smaller city) in the right panel. The horizontal axis shows the extent of ICT openness
4 ≡ τ −θ .

4.5

Multi-city Analysis

We now turn to a multi-city analysis to explore the heterogeneous effects of a reduction in
the fragmentation cost on city-level skill composition. The objective is to have a relatively
large number of cities to mimic the fact that the population of every city, even the largest
city, constitutes only a minor fraction of the total population, so a single city’s internet
improvement would not affect the other cities significantly. At the same time, we want toavoid simulating too many cities, which is computationally intensive but does not provide
additional insights in a qualitative fashion. To this end, we choose an eight-city scenario, in
which we consider the case in which all cities have the same housing supply and there are
four big cities and four small cities with technology parameters given as follows:
T1 = T2 = T3 = T4 > T5 = T6 = T7 = T8 .
The results are displayed in Figure 5. Figure 5a shows that if there is an internet improvement in a small city, say City 8, which reduces the bilateral fragmentation costs between
the city and all the other seven cities, then the share of managers decreases in City 8. The
22

intuition is that as a small city, the low skilled wage here is relatively lower. When the city
gets more connected with the rest of the nation, some managers in those bigger cities findit more profitable to relocate their production teams in the smaller city, which increases the
local demand for production workers there, giving rise to an inflow of the low-skill workers
in the smaller city. In contrast, Figure 5b shows that if there is an internet improvement ina big city, say City 4, which reduces the bilateral fragmentation costs between the city andall the other seven cities, then the share of managers increases in this city. The intuition isthat as a big city, the low skilled wage here is relatively higher. When the city gets moreconnected with the rest of the nation, some managers from smaller cities find it more profitable to relocate to that city themselves to leverage the strong agglomeration externalities
there, while keeping their production teams in other low-cost small cities. In doing so, larger
cities attract an inflow of high-skill labors.
These sets of results, together with the numerical simulations in the two-city case, illustrate our key theoretical result stated in Proposition 4. The logic behind this result can befound in a standard Ricardian model. When there is a drop in communication cost—i.e.,
trade cost—different regions specialize in the activities in which they have a comparativeadvantage. For larger cities, these are skill-intensive management-related tasks, whereas insmall cities, this corresponds to less skill-intensive standardized production. Given that factors are mobile within a country, changes to local labor demand driven by specialization
will imply a redistribution of high- and low- skilled workers across space, with larger cities
receiving an inflow of high-skilled workers and smaller cities an inflow of low-skilled workers.
In the next section, we provide empirical validation of the model prediction.

23

Figure 5: Eight-City Equilibrium
0.27

Share of Managers in City 8

0.26

0.25

0.24

0.23

0.22

0.21
0

0.1

0.2

0.3

0.4

0.5

ICT Openness

0.6

0.7

0.8

0.9

1

of City 8(a) Eight-City Equilibrium: Share of Managers

0.7

Share of Managers in City 4

0.65

0.6

0.55

0.5

0.45

0.4

0.35
0

0.1

0.2

0.3

0.4

0.5

ICT Openness

0.6

0.7

0.8

0.9

1

of City 4(b) Eight-City Equilibrium: Share of Managers
Notes: Figures 5a and 5b display the results of an eight-city simulation. In this simulation, we set θ = 5,
1
1
1
1
1
1
1
1
T1θ = T2θ = T3θ = T4θ = 1.5, T5θ = T6θ = T7θ = T8θ = 1.0, Lm = 1, Lp = 2, γ = 0.1, α = 0.4, β = 0.4,
H1 = H2 = H3 = H4 = H5 = H6 = H7 = H8 = 1.0. The vertical axes show the share of managers in City 4(the smaller city) in the top panel and that in City 8 (the larger city) in the bottom panel. The horizontal
axis shows the extent of ICT openness 4 ≡ τ −θ .

24

5Heterogeneous Effects of Internet Quality on City
Skill Composition: The Evidence

To validate the key theoretical results stated in Proposition 4, we next empirically investigate
the heterogeneous effects of fragmentation cost reduction on the share of high-skill employment across cities of different sizes. We focus on one channel: Improved internet quality
reduces bilateral fragmentation cost—e.g., by facilitating cross-city communication between
managers and production workers. In particular, our model predicts that local internet improvement drives up the high-skill employment share in bigger cities and reduces it in smaller
cities.

5.1

Empirical Specification

We examine these predictions by presenting evidence from U.S. cities. The empirical specification we employ a long difference exercise with the following specification:∆t ln = β1 + β2 ∆t qn + β3 (Ln,t0 × ∆t qn ) + γXn,t0 + n ,

(26)

 m

where ∆t ln ≡ ∆t LLnn is the change in high-skill employment share in city n between 1980
and 2013, Ln,t0 is the log of total labor supply in city n in 1980, ∆t qn is the change in internet
quality in city n between 1980 and 2013, and Xn,t0 is other controls including state dummies
and initial city size.
Our key parameters of interest are the coefficients on internet quality and the interaction
term between city size and internet quality, i.e., β2 and β3 . The model predicts that β2 < 0and β3 > 0, which imply that internet quality improvement in a small city will reduce theskilled employment share locally, while internet quality improvement in a big city will increase
the local skilled employment share.
As explained in Section 2, local internet quality is measured using FCC internet infrastructure data. Specifically, we first calculate the simple average of upload and download
down
bandwidths at the PUMA level, denoted by bup
in PUMA j of CZ n. The CZ-levelnj and bnj
internet quality measure, qn , is defined asdownlog(1 + bup
popnjnj ) + log(1 + bnj )
qn =
,
P
2
k∈G(n)popnkj∈G(n)

X

25

(27)

where G(n) is the set of PUMAs in CZ n and popnj is the population in PUMA j of CZ
n.23 Given that there is virtually no commercial use of the internet in 1980, qn in 2013 also
represents the change in internet quality from 1980 to 2013, i.e., ∆t qn ≡ qn . Figure 6 showsa map of internet qualities across CZs. Notably, there is large variation in internet quality
across different regions.

96.0 − 984.2
64.1 − 96.0
48.5 − 64.1
37.0 − 48.5
26.0 − 37.0
11.5 − 26.0

Figure 6: Average Internet Bandwidth in U.S. Commuting Zones
Notes: This figure displays the average internet bandwidth in the U.S. at CZ level, calculated as the
population-weighted average of upload and download bandwidths. Bandwidths are measured in megabytes
per second.

5.2

Internet Quality, City Size, and the Skilled Employment ShareUsing the internet data, we run the specification in (26). The first two columns of Table 4report the results. Columns (1) and (2) show the OLS results without and with state fixed
effects. Importantly, consistent with the model predictions, we find that β̂2 < 0 and β̂3 > 0.
Both are statistically significant at the 5% level. These two results jointly imply that betterinternet quality reduces a small city’s high-skill employment share and increases a big city’s
high-skill employment share, thereby confirming our model’s predictions.
An obvious problem that arises when estimating (26) using OLS is that internet quality is
endogenous. Specifically, there are three major concerns: First, there may be long-run local
23

Taking log reduces potential outliers within a CZ. Adding 1 to the measured bandwidths ensures that
down
when there is no internet available, bup= 0, we have qn = 0 as well.
nj = 0 and bnj

26

employment trends that drive both the internet provision and high-skill employment share.
Second, there may be unobserved local shocks that affect both internet quality improvement
and changes in high-skilled share over time. The third concern is reverse causality: Local
demand shocks for skills may drive internet provision. It is worth noting, however, that for
both the second and third points above, the potential bias must work in opposite directions
for larger vs. smaller cities to generate results consistent with theoretical predictions. For
example, for the reserve causality to work here, one must form a theory whereby local internet
quality improvement is driven by a larger share of high-skilled workers in bigger cities but
a lower share of high-skilled workers in smaller cities. Similarly, for the second concern,
the omitted variable must both increase internet quality and high-skill share in bigger cities,
while increasing internet quality and low-skill share in smaller cities.
To address the first concern, in Columns (4) and (5) of Table 4, we perform a falsification
test by replacing the left-hand-side variable with the change in the high-skill employment
share from an earlier period, between 1950 and 1980. The estimates show that there isindeed no role for later development of the internet in the change in skilled employment
share in earlier years, thus ruling out the existence of long-run local employment trends.
To address the second and third concerns, we consider an instrumental variable approach,using topographic elevation and initial telecommunication infrastructure before 1980 as theexogenous determinant in the provision of broadband internet. The use of geographic elements, such as topography, as a means for identification frameworks is common in many
empirical studies because of their generally random and predetermined nature, as we see in,e.g., Miguel, Satyanath and Sergenti (2004) and Juhasz and Steinwender (2018). In addition,
Jaber (2013) and Amorim and Sampaio (2016) adopt the use of terrain elevation specificallyas an instrument for broadband internet in the U.S., since it captures a substantial portion of the costs of building and maintaining cable infrastructure—which, unlike many otherdeveloped countries, is the most used technology for signal distribution in U.S. broadband
internet provision. The key intuition is that low-lying areas are more prone to floods andexhibit higher summer temperatures, and such climatic conditions play a crucial role in the
deployment and maintenance of cable broadband infrastructure. To formally establish thepredictive power of the instrument on internet provision, we use the following “stage-zero”
analysis:qn = α1 + α2 elevationn + α3 ini_telephone_penetrationn + Xn + n ,(28)

where qn is the population-weighted log of average upload and download speeds in CZ ndefined in (27), Elevationn is the population-weighted average terrain elevation in CZ n, and27

Xn includes city size and dummy variables for state fixed effects. Additionally, we control
for initial telephone penetration in the CZ, ini_telephone_penetrationn , which is calculated
as the average fraction of households that have access to telephones in 1970 and 1980 within
CZ n. In Table 3, we find that α̂2 = 0.193 and α̂3 = 2.849, both of which are statisticallysignificant at the 5% level. This shows that all else equal, places with higher terrain tend toreceive better internet, lending support to the relevance assumption of the instrument.
Dependent variable: Internet quality(1)(2)
elevation
0.214** 0.193**(0.085) (0.080)
initial telephone penetration
2.849***(0.656)
State Fixed EffectYY
Observations
722
722
R2
0.442
0.461
Table 3: Terrain Elevation, Initial Telephone Penetration and Internet Quality
Notes: This table reports the relationship between internet quality (year 2014) and terrain elevation andinitial telephone penetration (before 1980). Robust standard errors are in parentheses. City size and state
fixed effects are controls.

In addition to the relevance condition, the instrument must also satisfy the following
exclusion restriction: Terrain level must affect the change in skill share only through its
impact on internet quality. This is likely to hold for two reasons. First, while terrain is likely
correlated with other factors that may affect the level in the share of high-skilled workers
through other channels, it is unlikely that they affect the flow of high-skilled workers between
the two periods. For this to happen, the correlation between the instruments and these otherfactors will have to become stronger over time. Next, the correlations will also have to besystematically different across city sizes, i.e., the correlations are positive for larger cities(thereby attracting an inflow of high-skilled workers) and negative for smaller cities (thereby
resulting in an outflow of high-skilled workers).
Results from the 2SLS estimation, which are shown in Column (3) of Table 4 remain
qualitatively consistent from the OLS estimates. The point estimates of the coefficients on
qn and Ln,t0 × qn are greater in value than the OLS estimates. This may be due to classicalmeasurement errors in the regressors, which would result in attenuation bias. Crucially, themodel predicts that β̂2 < 0 and β̂3 > 0 continue to hold. In Column (6), we further apply
the 2SLS to our placebo test for the 1950-1980 change in the share of high-skill employment.
28

We draw a similar conclusion there is no long-run local employment trend that drives our
results on internet quality and high-skill employment share change.
Dependent variable: Change in the share of high-skill employment
1950-1980
1980-2013
OLS
2SLS
OLS
2SLS
(1)
(2)
(3)
(4)
(5)
(6)
Estimates
∗∗
∗∗
∗∗∗
qn
-.023
-.029
-.137
-.005 -.012 -.013(.009) (.012)(.034) (.017) (.020) (.037)∗∗∗∗
Ln,t0 × qn
.0022
.0028
.011∗∗∗ -0.000 .001
.001(.0008) (.0011) (.003) (.001) (.001) (.003)
State Fixed Effects
No
Yes
Yes
No
Yes
Yes
Observations
722
722
722
722
722
722
2
R
.045
.360
-0.076.048.284 -0.338
S-W F-stats (First Stage)
Internet quality
Internet quality × city size

12.92
11.15

12.92
11.15

Table 4: Heterogeneous Effects of Internet Improvement on Skill Shares Across Cities
Notes: City size is measured by log(labor supply in 1980) and is always included as a control variable.
Standard errors are in parentheses. Robust standard errors are used when there is no state fixed effect.
Standard errors are clustered at the state level when there are state fixed effects. We also report
Sanderson-Windmeijer (S-W) F-statistics for the first-stage regressions. ∗ p < 0.10, ∗∗ p < 0.05, ∗ ∗ ∗p < 0.01

6

Quantitative Analysis

Empirical validation of key model predictions lends credibility to our theoretical framework.
We next carry out quantitative analysis using the model. We first calibrate the model parameters, then conduct two counterfactual exercises by changing internet qualities in the US.
For both exercises, we consider the consequences of the counterfactual changes in internet
qualities on spatial skill distributions and real wages of high- and low-skill workers.

6.1

Parametric assumptions

For the quantitative assessment, we maintain the functional form assumption for the agglomm γ
eration force: f (Lmn ) = (Ln ) , where γ ≥ 0 is the parameter measuring the extent of regional29

agglomeration. Moreover, we parameterize the bilateral fragmentation cost as follows:log τnc = λnc + δ d log dnc + δ I qnc .

(29)

Equation (29) assumes that the fragmentation cost between two cities n and c takes a semiparametric form, i.e., a power function of the bilateral geographic distance dnc between thetwo cities and the quality of the internet connection between the two cities qnc , in addition
to a term λnc that summarizes all other associated costs—e.g., if the two cities are located in
the same state, and if the two cities share a common border. We refer to δ d as the distanceelasticity of joint production and δ I as the internet elasticity of joint production.
For the bilateral internet connection, we assume it adopts a quasi-symmetric form suchthat
qnc = qn × qc ,(30)
where qn is city n’s internet quality defined in (27). Note that by using the interaction term
qn × qc , we allow potential complementarity in both cities’ internet quality. For instance, if
there is no internet in city c, then the bilateral communication cost between c and n willremain very high, regardless of n’s internet quality.
One concern is that internet quality may also change trade cost in goods, which canpossibly change the skill distribution as well. In Appendix E, we empirically evaluate therole of internet quality in goods trade using the commodity flow survey data. We show thatthe internet does not have any significant impact on bilateral goods trade. Admittedly, theinternet has certainly changed the economy in many other ways in addition to reducing thefragmentation cost. However, focusing on the fragmentation cost is useful for understanding
the impact of the internet through this specific channel.

6.2

Calibration of Parameters

In this section, we calibrate model parameters. We begin by assigning values to parametersthat have been estimated in past literature. We then describe in detail the estimation procedures for the other parameters, including agglomeration externalities, dispersion of manager
productivity, city-specific housing supply, and technology parameter, as well as the fragmentation costs.

30

Parameters from Previous Literature
For some parameters in our model that are commonly used in the literature, we adopt theirvalues directly. Specifically, we use existing estimates for the values of the share of spending
on housing, 1 − α, and the span of control, β. We set 1 − α at 0.24 (Davis and Ortalo-Magné,
2011; Behrens, Duranton and Robert-Nicoud, 2014) and β at 0.53 (Buera and Shin, 2013).
See Table 5 for details.
Parameter
1−α

Value
0.24

β
γ

0.53
0.015

θ

4.11

δd

0.230

δI

-0.010Description
Share of spending
on housing
Span of control
Agglomeration externality

Moment / Source
Literature

Literature
Elasticity of worker
wage wrt city size
Frechét dispersion parameter High-skilled workers
income distribution
Distance elasticity of
Implied from gravity
joint productions
estimates
Internet elasticity of
Implied from gravity
joint productions
estimates

Table 5: Calibrated Model Parameters

Calibration of γ
The strength of agglomeration forces γ is set to target the elasticity of average worker wage
with respect to city size. The implied value of γ is 0.015, which is broadly in line withthe agglomeration externalities estimated in past literature (see, e.g., Combes and Gobillon,2015). In Appendix G, we conduct a sensitivity analysis to show that changing the value ofγ does not impact the results in a significant manner.24
24Note that γ is distinct from the observed productivity advantages of cities. In the model, larger cities
are more productive for three reasons: (1) the “raw” agglomeration externalities captured by γ; (2) the
exogenous productivity differences across cities implied by Tn ; and (3) the sorting of high- and low-skilledworkers because of fragmentation. Furthermore, γ is a term that summarizes multiple aspects of skill-biased
agglomeration externalities, including productivity, housing and amenities (Diamond, 2016).

31

Estimation of θ
The Frechét distribution parameter θ determines the dispersion of managers’ income acrosscities. From the cumulative distribution function of manager’s income in (12), we obtainγθ− log[− log G(π)] = θ(1 − β) log π + log[(Lmn ) Φn ] + constant.

(31)

We use the 3-year ACS 2011-2013 data to obtain the high-skilled hourly wage distribution.
Using the individual hourly wage information, we run an OLS regression with city fixedγθeffects, which absorbs the log[(Lmn ) Φn ] term. The OLS estimation then gives θ(1−β) = 1.93,
which implies a value of 4.11 for θ.
Estimation of Fragmentation Cost
Recall that the bilateral fragmentation cost is assumed to take the following functional form:log τnc = λnc + δ d log dnc + δ I qnc .
The key parameter of interest is δ I , the elasticity of fragmentation with respect to internet
quality. The estimation difficulty is that the aggregate cross-city fragmentation cost τnc is
not directly observed. To overcome this, we rely on the gravity equation derived in (9). We
first compute Xnc , the number of occurrences of the joint productions in city c that originate
from city n, by multiplying both sides of (9) by the total number of managers in origin cityLmn:−θ −βθ
wc
Tn τncXnc = Lm
.
(32)
n
Φn
Normalizing by Xnn and using the assumption that τnn = 1, we obtain the following
function that links τnc with city-level worker wages and Xnc :τnc =wcβθ Xnc
wnβθ Xnn

!−1/θ

.

(33)

Since wn is directly observed our data set, we can calculate τnc using additional information
on cross-city joint productions, i.e., Xnc . We rely on multi-locational production data tomeasure Xnc . The data are constructed using the Orbis Database, which reports ownership
information for subsidiary plants. We define a headquarters-subsidiary pair if a headquarters

32

has strictly more than 50% of the ownership of a given subsidiary. Moreover, the databasereports the locations of the subsidiary and the headquarters, which allows us to count the
number of headquarters-subsidiary pairs at the city-pair level. Specifically, for each city c,
we calculate Xnc by counting the number of subsidiaries that belong to headquarters locatedin a given commuting zone n.
Admittedly, these headquarters-subsidiary pairs by no means capture all of the cross-city
joint-production forms; e.g., firm’s domestic outsourcing is not included. However, given thisdata limitation, we view that this headquarters-subsidiary pair as a reasonable starting point
to study this question, for two reasons: First, the headquarters-subsidiary relationship fits thehigh-skilled and low-skilled joint production setting well in the theoretical part; and second,
it identifies a specific channel through which firms can achieve fragmented production.
Using the estimates of τnc from (33), we can estimate (29) using the following specification:log τnc = χn + ιc + δ d log dnc + δ I qnc + ΘHnc + εnc ,(34)

where χn and ιc are origin and destination fixed effects, respectively, dnc is the distance
between two cities n and c, qnc denotes the bilateral internet connectivity between city nand city c as defined in (30), and Hnc is a vector of city-pair controls, including state pair
fixed effects, the interaction between city sizes, dummies for two cities sharing a border,
dissimilarities in the language spoken, and racial mix.25
We estimate Equation (34) via OLS and PPML.26 Coefficient estimates δˆd and δˆI arereported in Table 6. We find that as expected, greater geographical distance reduces thenumber of headquarters-subsidiary pairs. More importantly, the result shows that a higher
quality of bilateral internet connectivity induces more headquarters-subsidiary pairs. Additional sensitivity analysis by changing the values of δ I is presented in Appendix H.
25

The dissimilarity in language spoken is constructed as follows: For each commuting zone, we use 1980
census data to calculate the fractions of people that speak English, Spanish, French, German, and otherlanguages at home. Then for any two commuting zones, we compute the Euclidean distance of the fractions.
The dissimilarity in race is constructed using four racial categories—white, black, native, and others—and
follow the same approach as in computing the dissimilarity in language spoken.
26
We use PPML to take into account the many zeros for the headquarters-subsidiary counts. We treat
1
1
the inverse of the fragmentation cost, τnc, as the dependent variable. τnc
is set to 0 when the count of
headquarters-subsidiary pairs is zero.

33

Dependent variable: Fragmentation cost between n and c (τnc )
OLS

PPML

(1)

(2)

(3)

(4)

log dnc

0.283***(0.002)0.134***(0.004)

0.588***(0.006)0.231***(0.006)qnc-0.048***(0.003)-0.010***(0.003)-0.030***(0.010)-0.010**(0.004)Controls
City Fixed Effects
N

No
Yes
44,188Yes
Yes
44,023

No
Yes
517,681Yes
Yes
505,008

Estimates

Table 6: Gravity Equation Estimates
Notes: Robust standard errors in parentheses. Significance levels: * 10%, ** 5%, ***1%. Controls include adummy on whether two CZs share a border, dissimilarity in language spoken, dissimilarity in race mix,
interaction between both two CZs’ size and state pair fixed effects.

Housing Supply Hn
Another set of parameters in the model is the exogenous housing supply, which is estimatedusing ACS 2011-2013 data on the average city-level wage wn for workers and total labor
income Wn of the city, i.e.,1

Hn
Wn /wn(1−α)
.
=
1
Hn0
Wn0 /wn(1−α)0(35)

We normalize the housing supply in CZ with code 00100 as 1—i.e., HCZ00100 = 1—and thencompute Hn for other cities using the ratio above.
City Technology Tn
The final step requires estimating the city-specific technology parameter Tn . Combining thedefinition for the city-level fragmentation potential Φn in (8) and the equilibrium condition
for manager’s living location choice
γ
Lm
1
Φn
pn
wn
log nm +log= (1 − α) log
= log
,
1−β
Lc
θ(1 − β)
Φc
pc
wc

34

we obtain:
β −θ
γ
Lm
Tn
1
1
wn
k (τnk wk )nlog m +
log
+
log P
.
β −θ = log
1−βLcθ(1 − β)Tcθ(1 − β)wc
k (τck wc )

P

(36)

−θ
Given the set of {Lmn , τnc , wn }, we can back out Tn . We normalize TCZ00100 = 1 and thenpick Tn so that the model-implied values for log TTnc match the corresponding values estimated.
Figure 7 shows the model-generated technology parameters. We can see that CZs with greater
technology parameters are concentrated in large cities (e.g., New York, San Francisco, andSeattle) and other denser areas along the coasts.

In our calibration, we have used the total labor income in each city, high-skilled labor’s
income distribution within the country, the number of high-skilled labor and low-skilledlabor’s wage in each city, which are directly from the data. Since in each city, the totallabor income equals the sum of the number of workers of each type multiplied by the average
income of each type. Our calibrated model should deliver a good match of the number of
low-skilled labor thus the total number of labor supply in each city. Figure 11 in Appendix
J confirms that this is indeed the case.

2.00 − 7.82
1.60 − 2.00
1.39 − 1.60
1.16 − 1.39
0.95 − 1.16
0.25 − 0.95
No dataFigure 7: City-specific Technology Parameters
Notes: The figure shows the model-generated technology parameter (Tn ) in 2013.

35

6.3

Internet Infrastructure, Skill Relocation, and Welfare

We first perform an exercise in which we assume there is no internet quality improvement
between 1980 and 2013. This counterfactual scenario allows us to evaluate the role of internet
infrastructure in the skill relocation in the U.S. through production fragmentation, and assess
the impact of internet improvement on welfare of high- and low-skilled workers.
Specifically, we first take the calibrated parameters in 2013 as given. We then solve themodel under two different sets of bilateral fragmentation costs. The first set of fragmentation
costs is directly obtained from the data in 2013 using equation (33). The second set offragmentation costs is derived by assuming a counterfactual scenario in which the cost τ̃nc isotherwise identical to the estimated cost except for internet connectivity—i.e.,τ̃nc = exp(log(τnc − δ̂ I qnc )).
The model is solved numerically under these two scenarios for 722 cities, using a global
method. Appendix F provides details of the numerical methodology.
We then compare the high-skill share in each city under the two scenarios. The reductionin the share of high-skilled workers informs us of the contribution of internet technology
in driving the observed changes in skill concentration across space. Figure 8 visualizes the
positive relationship between the change in high-skilled employment share and city size.
In the left panel, both the baseline scenario (with internet) and the counterfactual scenario(without internet) exhibit a positive slope. The flatter slope under the counterfactual scenario
shows that the extent of skill redistribution would have been smaller without internet quality
improvement. Formally, we regress the change in high-skill share on city size and obtain acoefficient of 0.0031 when state fixed effects are included, as shown in Table 7. Comparing
this against the observed skill redistribution reported in Table 1, it implies that without
internet connectivity, the observed skill redistribution in the US would have been reduced byabout 0.00310/0.00503 = 61%.
We also study the welfare implications of internet infrastructure through the lens of production fragmentation and find that its impact is sizable. With the internet, production
workers’ welfare (real consumption) increases by 3.62% and managers’ welfare by 3.39%.
The intuition is that the reduction in fragmentation cost is effectively technological progressfrom the whole economy’s point of view. Moreover, the reduction in fragmentation cost does
not exhibit skill bias and benefits the joint production of managers and production workers.
Therefore, it increases the welfare of managers and production workers in similar magnitudes.
Additionally, internet technological progress, as shown above, drives spatial reorganization
36

change in skilled share from without to with Internet
−.01
0

.01

.04
.02
skilled share
0
−.02
−.04

8

10
12
city size

without internet

14

16

−.02

6

6

with internet

8

10
12
city size

14

16

Figure 8: Simulated Relationship between High-skill Employment Share and City Size
Notes: This figure displays the model generated change in high-skill employment share when moving the
economy from the case without internet and with internet in 2013. City size is measured as log(labor
supply in 1980), as in regression Table 1.

Dependent variable:

City Size
State fixed effects
Observations
R2

Change in high-skill employment sharewith internet
(1)
(2)
∗∗∗
0.00320.0031∗∗∗(0.0007)(0.0009)
No
Yes
722
722
0.037
0.141

∗ p < 0.10, ∗∗ p < 0.05, ∗ ∗ ∗ p < 0.01

Table 7: Model-implied Change in High-skill Employment Share and City Size
Notes: The dependent variable is the change in high-skill employment share when moving the economy
from the case without the internet to the case with the internet. City size is measured by log(labor supply
in 1980). Column (1) reports results using robust standard errors, and Column (2) with standard errors
clustered by state.

37

of production, by changing local demand for and high- and low-skill workers across cities ofdifferent sizes. This spatial reorganization benefits workers of both skill types as well.
The welfare implications from internet improvement can be attributed to two channels:
the direct effect driven by the drop in the iceberg fragmentation cost τ , and the indirect
general equilibrium effect from spatial reorganization. We further decompose the welfarechanges into these two components. To get the first component, we fix all the production
teams in the scenario without the internet. Suppose that there are Lm
nc managers from citypn cooperate with Lnc production workers from city c to produce, calculated in the scenario
without the internet. The total output is also a function of the bilateral fragmentation cost1p
Snc (Lmτnc since it works as an iceberg cost in our model. We denote their output as τnc
nc , Lnc ),where Snc is the aggregate production function at the bilateral level (see Appendix I for thedetailed derivations of function Snc ). Since in each team, managers get 1 − β share of theoutput and production workers get β share of the output. We then compute the housing
price in any city n as the total income in city n divided by housing supply in city npxn =(1 − β)

P

P 1
1
p
p
m
m
x Snc (Lnc , Lnc ) + β
x Scn (Lcn , Lcn )
c τnc
c τcn

Hn

(37)

,

where x denote the two scenarios, "with internet" and "without internet." We then computethe log-change in the real income of managers and production workers under the two setswith internet
no internetof fragmentation cost τnc
and τnc. For managers, the change in real income
directly due to the drop in fragmentation cost isppX
Snc (Lm1
Snc (Lm
nc , Lnc )nc , Lnc )log (1 − β)− log (1 − β).
with internet (pwith internet )1−α
no internet (pno internet )1−αn,c τncn,c τncnn(38)
For production workers, the change in real income directly due to the drop in fragmentation
cost is

"

#

1

X

"

#

p
p
X
Scn (Lm1
Scn (Lmcn , Lcn )cn , Lcn )
−
log
β
.
log β
with internet (pwith internet )1−α
no internet (pno internet )1−αn,c τcnn,c τcn
n
n

"

X

1

#

"

#

(39)

The difference between the total changes in welfare and the above changes—which is the direct
welfare implications from internet improvement—gives the welfare change component due tospatial reorganization for managers and production workers, respectively. Table 8 reports thedecomposition of welfare changes. While the direct effect of the drop in the fragmentation
cost accounts for the major increase in both managers’ and workers’ real incomes, the generalequilibrium effect of spatial reorganization on welfare is also far from negligible. It accounts
38for more than one third of the welfare increase for managers and more than one fourth of thewelfare increase for production workers.
∆ Managers’ Welfare ∆ Workers’ Welfare
Directly Due to Fragmentation Cost Change
2.09%
2.63%
Due to Spatial Reorganization
1.30%
0.99%
Total
3.39%
3.62%
Table 8: A Decomposition of Welfare Change
Notes: This table shows the total welfare (real income) increase and decompose it to two components. The
first component is directly due to the change in fragmentation cost. The second component is the remaining
part and labeled as “due to spatial reorganization”.

6.4

Narrowing the Digital Divide

We perform another counterfactual experiment. Many governments and international organizations initiate programs that target improving internet access and internet quality forunderdeveloped areas to resolve the so-called “digital divide.” For instance, the Connect
America Fund in the U.S. is designed to expand access to voice and broadband services forareas where they are unavailable and perform network upgrades. As shown earlier, there arewidespread inequalities in the quality of internet provision across regions in the U.S. We areinterested in learning what the consequence on skill redistribution and welfare will be if areas
currently under served improve their internet quality so that a more uniform distribution ofinternet quality is achieved. To do so, we consider an experiment that upgrades the internet
in areas with below-median quality to the median level.
Table 9 shows the relationship between the model-generated change in high-skilled shareand city size after the more uniform internet quality improvement. The positive relationshipsuggests that on average, big cities will get relatively more of the high skilled, which drives
greater spatial divergence of skills across cities. The welfare implications are not negligible:
We find that production workers’ welfare would be raised by 0.19% and managers’ welfare by
0.17%. The welfare improvement is driven partly by the direct impact of better internet, anddriven partly by the general equilibrium effect—that is, mangers reorganize their production
teams’ spatial organization to leverage the comparative advantages of different cities. These
numbers suggest that improving internet quality for areas with a poor connection can bevery beneficial. The exercise provides a quantitative evaluation on internet infrastructure
investment that can be used for the benefit-cost analysis of policies that aim at narrowing
the digital divide.
39

Dependent variable:

City Size
State fixed effects
Observations
R2

Change in high-skill employment sharewith internet
(1)
(2)
∗
0.00032
0.00071∗∗∗(0.00019)(0.00021)
No
Yes
722
722
0.037
0.117

∗ p < 0.10, ∗∗ p < 0.05, ∗ ∗ ∗ p < 0.01

Table 9: Model-implied Change in High-skill Employment Share and City Size
Notes: The dependent variable is the change in high-skill employment share after a more uniform internet
quality improvement program. City size is measured by log(labor supply in 1980). Column (1) reports
results using robust standard errors, and Column (2) with standard errors clustered by state.

7

Conclusion

In this paper, we examine how domestic production fragmentation – facilitated by the improvement in ICT – drives the redistribution of skills. We document empirical facts on thechanging spatial distribution of the U.S. labor force. Between 1980 and 2013, the segregation of the high-skilled workers and low-skilled workers became more pronounced across U.S.
cities, with bigger cities attracting more high-skilled workers. This trend is more salient inindustries that are easier to fragment.
Based on these findings, we develop a model of production fragmentation in a systemof-cities setting with heterogeneous agents. Our model differs from other studies in similarsystem-of-cities settings, given our explicit emphasis on production organization structure
and cross-city production team formation. The model reveals the role of falling communication cost in shaping production fragmentation decisions and generates novel predictions
on spatial distribution of skills. We investigate the heterogeneous effect of U.S. internet infrastructure improvement on the skill composition of cities of different sizes, which is fully
consistent with the model prediction. Finally, our quantitative evaluation of the model using U.S. data shows that domestic production fragmentation, facilitated by improvements
in modern communications technology, is an important mechanism that drives the observed
spatial distribution of skills in the U.S. In addition, the proposed channel has positive andsizable welfare impacts on both the high-skilled and low-skilled workers.
Our paper abstracts from the role of firm boundary and adopts a simple production
organization structure with only two layers. Explicitly taking into account the boundary40

of firms and the multilayered hierarchy of production in geographic fragmentation might befruitful areas for future research.

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database].” Minneapolis: University of Minnesota.
Strauss-Kahn, Vanessa, and Xavier Vives. 2009. “Why and where do headquarters
move?” Regional Science and Urban Economics, 39(2): 168–186.
Tian, Lin. 2019. “Division of Labor and Productivity Advantage of Cities: Theory andEvidence from Brazil.” Unpublished Manuscript.
Tolbert, Charles M, and Molly Sizer. 1996. “US commuting zones and labor market
areas: A 1990 update.”

44Online Appendix
A

ProofsThis section provides proofs to results presented in Section 3.

A.1

Proof of Proposition 1

Proof. Denote Xnc = τ āncwβ , thennccβ −θ −θx

Gnc (x) = P r(Xnc ≤ x) = P r(ānc ≤ τnc wcβ x) = e−Tn (τnc wc ).

DefineX = max Xnc .
c

Then
−θ

−Φn x
Gn (x) = P r(X ≤ x) = ΠN.
c=1 Gnc (x) = e

The probability that city c provides the highest x to n is:
P r[Xnc ≥ max{xns ; s 6= c}] =where Φn ≡

A.2

Z ∞
0

Πs6=c [Gns (x)]dGnc (x) =Tn (τnc wcβ )−θ
,
Φn

β −θ
k Tn (τnk wk ) .

P

Proof of Proposition 2

Proof.
"P r(πn ≤ k) = P r β

β
1−β

1
1−β max {((1 − β)[f (Lm
n )]
c



1
ānc 1−β}≤kβ)τnc wc#= P r max ānc ≤ β −β (1 − β)−(1−β) τnc wcβ k 1−β /[f (Lm
n )]
c

m

θ

= e−[f (Ln )] Φn [β−β (1−β)−(1−β) ]−θ k −θ(1−β)

45

.

A.3

Proof of Proposition 3

Combining equations (24) and (25) by eliminating log wn − log wn0 , we obtain that
[1 + γ −

γ
1
1
Tn
m
][log Lm− 1] log.
n − log Ln0 ] = [
1−α
1−α
θ
Tn0

Therefore,mlog Lmn − log Ln0 = κ[log Tn − log Tn0 ],

(40)

where
κ=

1
−1 1
1−α
> 0,
γ
1 + γ − 1−αθγgiven that 1 + γ > 1−α.

That is,
Tn
Lm
n
=
m
Ln0
Tn0


κ

Then we get thatκLmn ∝ Tn .

(41)

From equation (24), we have11m
log wn − log wn0 = γ[log Lmn − log Ln0 ] + [log Tn − log Tn0 ] = [γκ + ][log Tn − log Tn0 ].
θθAnd from equation (19), we have workers’ mass in city n is given by1

Lpn ∝ wn−1 Tn wn−βθ Tnθ(1−β)−11−βθ[ θ(1−β)
−1]

wn

γ

+1
1−β
(Lm
.
n)

We can combine the above three equations to arrive at
Lpn ∝ Tnκ .

(42)

It is then also clear that given a set of {Tn }, the equilibrium exists and is unique.
The skill premium is read directly from equation (56). When τnc → ∞, ∀ n 6= c, it is
written as
1γ
11log Lmlog Tnθ −log wn .
n +
1−β
1−β
1−β

46

From equation (19), we get
1plog wn = log Tnθ + (γ + 1 − β) log Lmn − (1 − β) log Ln + (1 − β) log η.

The skill premium is then equal to a constant. Note that η is only a function of β and θ. So
the skill premium is irrelevant with γ.

A.4

Proof of Proposition 4

Proof. If ∆ is very small, we can do a first-order expansion with respect to ∆ around ∆ = 0.
1
1
1
1
γ
γ
[∆wβθ − βθ log w − ∆w−βθ ] +[log T1θ Lm− log T2θ Lm
12 ] = log w
θ(1 − β)
1−β

!

β
γ
1
m
log w = −log w +
+ 1 [log Lm
1 − log L2 ]
1−α
1−β
1−β
1
1
1
+
[log T1θ − log T2θ ]+
1−β
!

1
η
1
(wβθ − w−βθ ) +(w−βθ − wβθ + − x) ∆,θ(1 − β)
η+ζ
x
where
T1
x=
T2


1
 θ(1−β)βγ

w− 1−β +βθ lm 1−β +1 .

That is,1
1
1
log w = γ log lm + log T1θ − log T2θ + ∆(wβθ − w−βθ )
θ

!

β
1
+
log w =
1−α 1−β!

11γ1+ 1 log lm +[log T1θ − log T2θ ]+
1−β
1−β

!

1
η
1
(wβθ − w−βθ ) +(w−βθ − wβθ + − x) ∆.
θ(1 − β)η+ζx47

They lead to
1
1
1
α
β
γ
) log lm =[log T1θ − log T2θ ] ++(γ + 1 −1−α1−α1−α 1−β!

1 βθ
(w − w−βθ )∆
θ

!

1
η
1
−
(wβθ − w−βθ ) +(w−βθ − wβθ + − x) ∆.
θ(1 − β)η+ζxThat is,11αγ
α 1 βθ
) log lm =[log T1θ − log T2θ ] +(w − w−βθ )∆
1−α
1−α
1−αθ
η
1
−
(w−βθ − wβθ + − x)∆.
η+ζx(γ + 1 −By expanding w and x around ∆ = 0, we finally arrive at
1
1
γ
α
α 1
η
) log lm =[log T1θ − log T2θ ] + [+](ŵβθ − ŵ−βθ )∆1−α1−α1−αθ η+ζ1+ (x̂ − )∆x̂(γ + 1 −

where
T1
x̂ =
T2


α
 θ1 (1−β)(1+βθ+ 1−α
)

> 1,

and
T1
ŵ =
T2


 θ1

1
γ
γ+1− 1−α>1are solutions to x and w when ∆ = 0.
Thus, managers will relocate to the bigger city with internet improvement. It is also easy
to see that log w increases and log p increases locally with internet improvement. Moreover,
we examine the role of agglomeration force γ from the following:∂ log lm
1
α 1
η
1
=
[
+
](ŵβθ − ŵ−βθ ) + (x̂ − ) .
γ∂∆
γ + 1 − 1−α 1 − α θ η + ζx̂"#A larger γ implies a bigger reallocation of high-skilled to the bigger city.

48

Also,
1

−1

γ

m

1

+1

−1

m

γ

+1

Lp1
ηw1−1 T1 (w1β )−θ Φ1θ(1−β) L1 1−β + ηw1−1 T2 (w1β )−θ ∆Φ2θ(1−β) L2 1−β=.
1
1−1 m γ +1−1 m γ +1
Lp2
ηw2−1 T2 (w2β )−θ Φ2θ(1−β) L2 1−β + ηw2−1 T1 (w2β )−θ ∆Φ1θ(1−β) L1 1−β
Then
1

−1

γ

1

−1

γ

θ(1−β)
m 1−β +1
T11 /T22 w−1 (wβ )−θ Φ12(Lm+ T2−θ /T2−θ w−1 (wβ )−θ ∆Lp1
1 /L2 )
=
1
γ
−1
Lp2
θ(1−β)
m 1−β +1
1 + T1 /T2 ∆Φ12(Lm
1 /L2 )lp =θ(1−β)
T1 /T2 w−1 (wβ )−θ Φ12m 1−β +1
(Lm
+ T2 /T2 w−1 (wβ )−θ ∆1 /L2 )1

θ(1−β)
1 + T1 /T2 ∆Φ12



lp =

T1
T2



w−1−βθ



Φ1
Φ2



T1
T2



1+



−1

1
−1
θ(1−β)

Φ1
Φ2



γ

m 1−β +1
(Lm
1 /L2 )
γlm 1−β +1 + w−1−βθ ∆1−1θ(1−β)

γ.

lm 1−β +1 ∆When the cross-city communication cost is infinite,1ˆlp = T1 ŵ− 1−β
T2







T1
T2

1
 θ(1−β)
−1

γ
+1
1−β

ˆlm



=

T1
T2

 θ1

α
1−α
γ
γ+1− 1−α.

That gives

log lp =α1−αγ
γ + 1 − 1−α

1
θ

1
θ

[log T1 −log T211  θ(1−β)
 − θ(1−β)
β
β
γ
γ
T
T
1
1
]−
w− 1−β +βθ lm 1−β +1 −w 1−β −βθ lm − 1−β −1  ∆T2

T2

which leads tolog lp =

α
1−α

1
θ

γ [log T1
γ + 1 − 1−α

1

h

i

− log T2θ ] − ŵ1+βθ ˆlp − ŵ−1−βθ ˆlp−1 ∆.

It is clear that ∆ increase will drive production workers from big cities to small cities. Moreover, we examine the role of agglomeration force γ from the following:hi∂ log lp
= − ŵ1+βθ ˆlp − ŵ−1−βθ ˆlp−1 .
∂∆A larger γ implies a bigger reallocation of the low skilled to the smaller city.

49

B

Skill Premium and Welfare in the Two-city Case

This section presents welfare analysis for a two-city version of the baseline model presented
in Section 4.4.
We first do a first-order expansion around ∆ = 0. The skill premium is
1γlog Lmlog Φ1 − log w1
1 +1−β(1 − β)θ
1
γ1=log Lm[log T1 + log(1 + ∆wβθ )] −log w11 +
1−β(1 − β)θ
1−β
γ
1
1
=
log Lm[log T1 + (1 + ∆ŵβθ )] −log w1 ,1 +
1−β(1 − β)θ
1−β

sp =

(43)

where w = w1 /w2 .
Note that the market-clearing condition for production workers is1

T1 Φ1θ(1−β)

−1

1

γ

+1
1−β
Lm
(w1−βθ−1 + ∆w2−βθ−1 ) + T2 Φ2θ(1−β)
1

−1

γ

+1
1−β
Lm
(w2−βθ−1 + ∆w1−βθ−1 ) =
2

Lp
.
η

That is,
1

γ

1

+1
1−β
T1θ(1−β) (w1−βθ + ∆w2−βθ ) θ(1−β) −1 Lm(w1−βθ−1 + ∆w2−βθ−1 )
1
1

γ

1

+1
1−β
+T2θ(1−β) (∆w1−βθ + w2−βθ ) θ(1−β) −1 Lm(∆w1−βθ−1 + w2−βθ−1 ) =
2

Lp
.
η

(44)

Rearrange to get
11T1θ(1−β) (1 + ∆wβθ ) θ(1−β) −1 (1 + ∆wβθ+1 )1

1γm − 1−β −1+T2θ(1−β) (∆ + wβθ ) θ(1−β) −1 (Lm(∆ + wβθ+1 ) =1 /L2 )1γ
Lp 1−β
− 1−β
−1
w1 Lm
.
1
η

Recall that
1
1
γ
α
α 1
η
) log lm =[log T1θ − log T2θ ] + [+](ŵβθ − ŵ−βθ )∆1−α1−α1−αθ η+ζ1+ (x̂ − )∆x̂(γ + 1 −50(45)

where
T1
x̂ =
T2


α
 θ1 (1−β)(1+βθ+ 1−α
)

> 1,

and
T1
ŵ =
T2


 θ1

1
γ
γ+1− 1−α>1are solutions to x and w when ∆ = 0. Therefore,
γ
γ
1
1
+1
+1
α
γ
α 1
η
1−β
1−β
m
θ
θ
(−
− 1) log l=−[log T1 − log T2 ] −
+
]
γ
γ [
1−β
γ + 1 − 1−α 1 − α
γ + 1 − 1−α 1 − α θ η + ζ

(ŵ

βθ

− ŵ

−βθ

γ
+1
1
1−β
)∆ −
γ (x̂ − )∆.
γ + 1 − 1−αx̂This implies that
γ

+1

α 1
− γ −1T1 − 1−β γ 1−αθlm 1−β = ( ) γ+1− 1−α
T2

#
γ
γ
+1
+1
α 1
η
1
1−β
1−β
βθ
−βθ
+
](ŵ − ŵ )∆ −1−γ [γ (x̂ − )∆ .
γ + 1 − 1−α1−αθ η+ζγ + 1 − 1−αx̂"As a result,
γ

+1

α 1
1
1
1
T1 − 1−β γ 1−αθT1[1 + (ŵβθ (×− 1) + ŵβθ+1 )∆] + T2θ(1−β) ŵβθ( θ(1−β) −1) ŵβθ+1 ( ) γ+1− 1−αθ(1 − β)
T2
γ
γ
+1
+1
α 1
1
η
1−β
βθ
−βθ
(1 + ŵ−βθ ∆ + ŵ−βθ−1 ∆ − 1−β
[
+
](
ŵ
−
ŵ
)∆
−
γ
γ (x̂ − )∆)γ + 1 − 1−α 1 − α θ η + ζ
γ + 1 − 1−αx̂1θ(1−β)=1γ
Lp 1−β
− 1−β
−1
w1 Lm
.
1
η

(46)

We can then obtain that1γ
log w1 − (+ 1) log Lm
1 = constant +
1−β
1−β

A
1
θ(1−β)T151

1
θ(1−β)

+ T2

w

1
1−β

−

( TT12 )

γ
+1
1−β
α 1
γ
γ+1− 1−α 1−α θ∆,where
γ

+1

α 1
1
1
1
T1 − 1−β γ 1−αθ− 1) + ŵβθ+1 ) + T2θ(1−β) ŵβθ( θ(1−β) −1) ŵβθ+1 ( ) γ+1− 1−α
A = T1(ŵβθ (×θ(1 − β)
T2
"
#
γ
γ
+1
+1
α 1
η
1
1−β
1−β
−βθ
−βθ−1
βθ
−βθ
ŵ
+ ŵ
−
+
](ŵ − ŵ ) −γ [γ (x̂ − ) .
γ + 1 − 1−α1−αθ η+ζγ + 1 − 1−αx̂1θ(1−β)(47)
Since the skill premium is
11γ[log T1 + (1 + ∆ŵβθ )] − (log w1 −log Lm1 ),(1 − β)θ
1−β
1−β
we know that the sign of the skill premium is the same as the sign ofγ1θ(1−β)

T1

(ŵ

βθ

− ŵ

βθ+1

1
θ(1−β)) + T2ŵ

1βθ( θ(1−β)
−1)

γ

+1

α 1
T1 − 1−β γ 1−α1θŵβθ+1 ( ) γ+1− 1−αŵβθ −
×T2(1 − β)θ

+1

α 1
T1 − 1−β γ 1−α
θ
T2
ŵ
×
ŵβθ+1 ( ) γ+1− 1−α
T2
"
#
γ
γ
+1
+1
α 1
η
1
1−β
1−β
−βθ
−βθ−1
βθ
−βθ
ŵ
+ ŵ
−
+
](ŵ − ŵ ) −γ [γ (x̂ − ) .
γ + 1 − 1−α1−αθ η+ζγ + 1 − 1−αx̂1θ(1−β)1βθ( θ(1−β)
−1)

(48)
The sign can be positive or negative.
Managers’ welfare is
1γlog Lmlog Φ1 − (1 − α) log p1 .
1 +1−βθ(1 − β)(49)

Since housing price is given bylog p1 = log(1 − α) + log W1 − log H1 ,

(50)

where
γ

1

θ(1−β)1−β Φ
W1 = w1 Lp1 + ζLm
Lm
1
1
1 ,

52

(51)

managers’ welfare is rewritten as1γ1γm 1−β θ(1−β) m
1
+
+
ζL
Φ
log Lm
log
Φ
−
(1
−
α)
log
w
−
log(L
L1 /w1 )
1
1
1
1
1
p
1−β
θ(1 − β)γ

1θ(1−β)1−β ΦLm= skill_premium + α log w1 − log(L1p + ζLm
1
1 /w1 ).
1(52)p
Similarly, we can substitute expressions for the skill premium, log w1 , Lm
1 , and L1 derived
welfareabove, to get ∂ managers’
evaluated at ∆ = 0. Finally, production workers’ welfare is∂∆equal to managers’ welfare minus the skill premium.

C

Equilibrium Characterization

In this section, we show, using Banach fixed point theorem, a set of sufficient conditions
under which the equilibrium exists and is unique. For simplicity of exposition, we denote−θ. For the derivation of analytic results, we follow the conventional literature∆nc = τnc
and adopt the following parametric assumption for the city-level agglomeration forces for
managers (see, e.g., Allen and Arkolakis, 2014):
f (L) = Lγ , where γ > 0.
Combining this assumption and the equilibrium housing prices in (11), we can rewrite theindifference conditions for workers and managers in (15) and (16) as
Lm
1
Φn
pn
wn
γ
n
log m
+
log
= (1 − α) log
= log
1−β
Lc
θ(1 − β)
Φc
pc
wc

(53)

and


wn
wc

1

 1

1−α

=

γθ
ζ(Lm
Φn ) θ(1−β) Lm
n
n +

P

kη

1
P
γθ
ζ(Lm
Φc ) θ(1−β) Lm
c
kη
c +

1



Tk (τkn wnβ )−θ Φkθ(1−β)

Tk (τkc wcβ )−θ

m



−1

1
−1
θ(1−β)

Φk

γ

+1
1−β
[Lm
Hc
k ]

+1 Hn
1−β
[Lm
k ]
γ

.

(54)

n
We can then solve for wwnc and LLmfrom the above two equations. In a special case with nocagglomeration force γ = 0, we can first solve worker’s wage wn from equation (53) and then
the number of managers Lm
n from equation (54).

53The relative number of production workers in city n and city c is given by
1





−1

γ

+1
−1
1−β
Tk (τkn wnβ )−θ Φkθ(1−β) [Lm
Lpn
k ηwn
k ]
=
.
1


γ
−1
P
Lpc
β −θ
θ(1−β)
m 1−β +1−1
Tk (τkc wc )
[Lk ]
Φk
k ηwc

P

(55)

Finally, the skill premium, defined as the log difference between the manager’s and production worker’s expected income, is given by:
log E[πn ] − log wn =1γlog Lmlog Φn − log wn .
n +1−β(1 − β)θ

(56)

Proposition 5 (Existence and Uniqueness) If there exists an aux ∈ R such that
1−β
+1
1
−βθ
−βθ + auxγ|+|
| + |(1 + )()| < 1,ρ=|
1/(1 − α) + aux
1/(1 − α) + auxθγ 1/(1 − α) + aux

then the spatial equilibrium exists and is unique.
Proof. We obtain the following equation from the definition of Φn in (8):∆ T
 11 1 ∆21 T2

..


.

∆12 T1∆22 T2..
.

∆13 T1∆23 T2
..
.

...
...
..
.



∆1N T1Φw−βθ
 1 1   −βθ ∆2N T2  w2   Φ2 





..
  ..  =  ..  .
 .  . 
.

∆N 1 TN ∆N 2 TN ∆N 3 T2 . . . ∆N N TN

















−βθ
wN

ΦN

(57)

From equation (53), we get
m

γ

−

1

Ln 1−β ∝ wn Φn θ(1−β) .

(58)

Therefore, up to a constant, and using results from equation (54), we can rewrite the54matrix as1θ(1−β)1−1
θ(1−β)








1
−1
θ(1−β)1−1
θ(1−β)

ηT2 ∆21 w1−βθ Φ2+ ηT1 ∆11 w1−βθ Φ1ζΦ11θ(1−β)

ηT1 ∆12 w2−βθ Φ1
..
.

ζΦ2

1
−1
θ(1−β)1−1
θ(1−β)−βθηT2 ∆2N wN
Φ2−βθηT1 ∆1N wN
Φ1



1−β

1
1
− θγ
− θ(1−β)1−1
θ(1−β)+ ηT2 ∆22 w2−βθ Φ2..
.

ηTN ∆N 1 w1−βθ ΦN

1−1θ(1−β)



...
...
..
.

ηTN ∆N 2 w2−βθ ΦN
..
.

1
−1
θ(1−β)








...

1
θ(1−β)ζΦN

1−1
θ(1−β)−βθ+ ηTN ∆N N wN
ΦN



 1

w 1−α H 1−β +1 − 1 − 1   1 1 1 
w γ
θγ 
θ(1−β)
w21−α H2 
Φ2

=
.
× 2
 
..
.



 
..

.


1
w1 γ

1−β

wNγ

+1

+1

Φ1

1
1
− θγ
− θ(1−β)

(59)

1−α
wN
HN

ΦN

Multiply both sides by wnaux , where aux ∈ R is an auxiliary parameter, and we get1θ(1−β)



ζΦ1

1
−1
θ(1−β)

w1aux + ηT1 ∆11 w1−βθ Φ1
1−1
θ(1−β)








ηT1 ∆12 w2−βθ Φ1
..
.

w2aux

1
−1
θ(1−β)−βθηT1 ∆1N wN
Φ1



1−β

w1 γ

+1

1
− θ(1−β)

Φ1


− 1
θγ



w1aux

aux
wN
1

w11−α

ηTN ∆N 1 w1−βθ ΦN

w1aux

...
..
.

ηTN ∆N 2 w2−βθ ΦN
..
.

w2aux

...

+aux

H1

1
−1
θ(1−β)...

1−1
θ(1−β)1
θ(1−β)

ζΦN



1
−1
θ(1−β)−βθaux + ηT ∆wN
N N N wN ΦN







aux
wN



 1−β +1 − 1 − 1   1 +aux 
w γ
θγ 
θ(1−β)
w 1−α
H2 
Φ2

 
 2
.
=
× 2

.
.



 
..
..



1
1−β

wNγ

+1

Denote xn =

1
1
− θγ
− θ(1−β)

1−α
wN

ΦN



1
+ aux
1−α

Fi (x) = log[



X 1
j

Hi

+aux

(60)

HN

log wn and x = (x1 , x2 , ...xN )0 . Thenη exp(xi )−βθ+aux1/(1−α)+aux

Tj ∆ji exp(xj )

1−β
γ +1
1/(1−α)+aux

1−β

γ +1+aux11+ζexp(xi ) 1/(1−α)+aux (Φai )− θγ ],
Hi

where
Φaj = TjX−βθ

∆jk exp(xk ) 1/(1−α)+aux .

k

55



Φaj

−1− 1θγ

Finally, we can show thatd(F (x), F (y)) = max |Fi (x) − Fi (y)|i= max log[i

λj exp(xi − yi )−βθ+aux1/(1−α)+aux

−βθ

T
 j

P

Tj

P

where

exp(xj − yj )

1−β
γ +1
1/(1−α)+aux

j



×

X

1
−1− θγ

1/(1−α)+aux
k ∆jk exp(xk )+ λN +1 exp(xi − yi )

−βθ

1−β
γ +1+aux
1/(1−α)+aux

−βθ



×

T
 j

P

Tj

P

1/(1−α)+aux
k ∆jk exp(yk )k ∆jk exp(yk )−βθ1/(1−α)+aux

j λj + λN +1 = 1, λj ≥ 0, λN +1 ≥ 0. Note that

P

Tj
Tj

P

k ∆jk exp(xk )Pk ∆jk exp(yk )−βθ1/(1−α)+aux−βθ
1/(1−α)+aux

≤

X

−βθ

ωk exp(xk − yk ) 1/(1−α)+aux

k

where
X

ωk = 1, ωk ≥ 0.

k

Therefore, we get thatd(F (x), F (y)) ≤ ρ · maxk |xk − yk | = ρ · d(x, y),
where
1−β
+1
−βθ + aux
1
−βθ
γ
ρ=|
|+|
| + |(1 + )()|.
1/(1 − α) + aux
1/(1 − α) + auxθγ 1/(1 − α) + aux

If there exists a real number aux such that ρ < 1, using Banach fixed-point theorem, theequilibrium exists and is unique.

D

Demand for Production Workers

We derive the labor demand for production workers given by equation (19).
Denote Xnc = τ āncwβ . Then from Proposition 1, we getncc

β −θ −θx

Gnc (x) = P r(Xnc ≤ x) = P r(Anc ≤ τnc wcβ x) = e−Tn (τnc wc )
56

1
− θγ

1/(1−α)+aux
k ∆jk exp(xk ).

The joint distribution whereby a manager from city n locates her production team in city cand that τ āncwβ = x isncc

P r(argmaxk

Given lnc = β

1
1−β

ānc
ānk
β −θ −θ−1 −Φn x−θe.
β = c∩
β = x) = θTn (τnc wc ) x
τnk wkτnc wc11−βwc−1 [f (Lmn )]1
Lpnc = β 1−β





ānc
τnc wcβ

 1

1−β

1
1−β Lmwc−1 [f (Lmnn )]Tn (τnc wcβ )−θ







1

= ηwc−1 Tn (τnc wcβ )−θ Φnθ(1−β)
1where η = β 1−βE, we have−1 hZ ∞ 

θx−θ−1 −Φn x−θ

e



x

1
1−β



dx ,

0
1

1−β Lm[f (Lmnn )]iR∞ − 1y θ(1−β) e−y dy.
0Internet Quality and Bilateral Goods Trade

We draw data from the Commodity Flow Survey (CFS) 2012, which is publicly accessible.
The survey records the value of shipments from region i to region j, where each region isdefined as a combined statistical area (CSA) in the U.S.. Supplementing these data with thegeographic information and internet quality data, we run the following regression:log(shipmentij ) = β0 + β1 log(distanceij ) + β2 qi ∗ qj + Xij + ij ,(61)

where the dependent variable is the logarithm of the total value of the shipment from CSA i
to CSA j, distanceij is the great circle distance, and qi is internet quality at the CSA i. We
perform the regression with and without location fixed effects.
Table 10 reports the results. In Column (1), we don’t include origin and destination
fixed effects, but include internet quality in i and j as additional explanatory variables. We
find that while bilateral distance significantly reduces trade, the impact of the internet on
bilateral goods trade is not statistically significant. In Column (2), we include both origin
and destination fixed effects. Similarly, the point estimate for bilateral internet connection
term qi ∗ qj is even smaller and is still statistically insignificant.

57

Dependent variable log(shipment)(1)log (distance)qi ∗ qjqi
qj
CSA Fixed EffectsNlog(shipment)(2)-1.236***(.0026).058(.094).489( .349).379(.356)-1.239***( .027).039(.053)

No
4,801

Yes
4,801

Table 10: Gravity Equation Estimates for Trade in Goods
Notes: Robust standard errors in parentheses. Significance levels: * 10%, ** 5%, ***1%.

58

F

Solution Algorithm for the Spatial Equilibrium−θ
For a system of N ≥ 1 cities, given a set of bilateral fragmentation cost τnc (or ∆nc = τnc),
technology Tn , housing supply Hn , and aggregate labor supply Lp and Lm , we use the following iteration methods (global methods) to solve the spatial equilibrium:(1) Pick up an initial set of production worker’s (relative) wage wr(0) (a vector of N − 1
dimensions), where wr(j) = w(j) (1 : N − 1)/w(j) (N ). For example, all N − 1 elements of wr(0)are set to 1.
(2) Pick up a real number aux. If the code doesn’t converge, pick up another aux and retry
the steps that follow. Start from j = 0.
(3) From equation (8), which defines Φn , we calculate relative Φr (a vector of N − 1 dimensions), where Φr(j) = Φ(j) (1 : N − 1)/Φ(j) (N ).
(4) Substitute vectors wr(j) , Φr(j) into the left-hand side of equation (60) to update vector
w on the right-hand side. The updated relative wage is written as wr(j+1) .
(5) Check convergence, if maxk=1,2,...,N −1 |wr(j) (k) − wr(j+1) (k)| ≤ , where, for example,
 = 10−6 . Then stop. Otherwise, go back to step (3) and continue.
(6) From equation (53), which gives managers’ spatial distribution, we get the relative number of managers Lrm (a vector of N − 1 dimensions), where Lrm = Lm (1 : N − 1)/Lm (N ).
(7) With the total supply of managers Lm and relative number of managers Lrm , we obtain
the equilibrium spatial distribution of managers. Equation (55) gives the relative number of
production workers. With the total supply of production workers Lp , we get the equilibrium
spatial distribution of production workers.
(8) The level of worker wage w is solved using the market-clearing condition for production
workers; see equations (18) and (19).
(9) With the expected income of managers living in city n (see equation (13)), worker wage,
number of managers, and number of production workers, we can add up the total income
Wn in a city. Combined with information on housing supply Hn , we get housing pricepn = (1 − α)Wn /Hn .
(10) Worker utility and managers’ expected utility are derived as wn /p1−αand E[πn ]/p1−α
n
n .

G

Sensitivity Analysis γ

Recall that γ in our model is calibrated to match the (average) worker wage elasticity withrespect to city size. In our equilibrium analysis in Proposition 4, we argue that larger γ will
imply more skill redistribution to larger cities (cities with greater technology parameter Tn ),59

given the same magnitude of communication cost reduction. We next evaluate how our key
quantitative results are sensitive to decreasing the value of γ.
In the baseline analysis, we set γ = 0.015. We further reduce its value such that γ = 0.005
and 0.010.27 We report the quantitative results in Table 11, including the slope of regressing
the change in the high-skilled share on city size and welfare (real consumption) change forboth managers and production workers.
It turns out that changing γ has very little impact on the results. The slope of regressing
the change in the high-skilled share on city size actually becomes slightly smaller when γ
increases, if anything. This is precisely because of the re-calibration of Tn .28 Equation (36)tells us that
Tn
wn
1
Lm
(τnk wkβ )−θ
γ
1
n
log
= log
−
log Pk
log
.
−
β −θ
m
θ(1 − β)Tcwc
θ(1 − β)1−βLck (τck wc )P

(62)

Without loss of generality, consider a big city n, which usually has a relatively larger worker
wage wn and more supply of high-skilled Lm
n . A larger γ will reduce the value of the calibrated
Tn (Tn /Tc ). This means that big cities’ comparative advantage is weakened. Therefore, theimpact of a reduction in communication cost will be smaller. The two forces – a larger γ anda smaller Tn for big cities – will offset each other to some extent. As a result, changing γ
has very little impact on how communication cost reduction affects the skill redistribution.
Similarly, the welfare increases (change in log real consumption) for both managers andproduction workers change little with the value of γ.
γ
0.005
0.010
0.015 (benchmark)slope of skilled share change
w.r.t. city size
0.00300.00310.0032∆ workers’ welfare ∆ managers’ welfare
3.62%
3.62%
3.62%

3.39%
3.39%
3.39%

Table 11: Sensitivity of Changing the Strength of Agglomeration γ
Notes: This table shows how different values of the strength of agglomeration γ impacts ourquantitative results. ∆ workers’ welfare and ∆ managers’ welfare are changes in log realconsumption.

27

When we change the value of γ, we also need to redo the calibration of technology parameter Tn derived
from equation (36), since it will be affected by the value of γ.
28
Table 12 in the Appendix reports quantitative results without recalibrating Tn as a thought experiment.

60

H

Sensitivity Analysis δI

In our baseline exercise, we directly take the estimate of δI , the elasticity of fragmentation
cost with respect to bilateral internet quality, from a gravity equation test. We emphasize
the role of internet in shaping bilateral fragmentation cost by varying the value of δI in thissection.
The baseline exercise gives the value δI = −0.010. We try other two values, -0.005 and-0.015, which are half and double the baseline value. The results on skill relocation andwelfare are summarized in Table 12.
Changing how the internet shapes fragmentation cost δI drastically reshapes skill relocation and welfare change. When δI = −0.005, the change in the elasticity of the high-skilledshare with respect to city size drops to 0.0019 from 0.0031 in the baseline, which is a nearly
40% drop. Similar magnitudes of drops occur in both production workers’ and managers’
real consumption levels. When δI = −0.015, the opposite happens. The elasticity of thehigh-skilled share with respect to city size increases to 0.0042 from 0.0031, which is around a
35% increase. The welfare changes are even larger for both production workers and managers
are of the similar scales of increase.
δI-0.005-0.010 (benchmark)-0.015slope of skilled share change
w.r.t. city size
0.00190.00310.0042∆ workers’ welfare ∆ managers’ welfare
2.04%
3.62%
4.85%

1.89%
3.39%
4.56%

Table 12: Sensitivity of Changing the Elasticity of Fragmentation Cost w.r.t. Internet Quality
δI
Notes: This table shows how different values of the elasticity of fragmentation cost withrespect to internet quality δI impacts our quantitative results. ∆ workers’ welfare and ∆managers’ welfare are changes in log real consumption.

61

I

Derivation of Production Function Snc

We have the following conditional probability derived in Appendix D
P r( τ āncwβ = x, argmaxk τ ānkwβ = c)
ānc
ānk
−θ
nc c
nc c
= θx−θ−1 e−Φn x Φn .
P r(
ānk
β = x|argmaxk
β = c) =P r(argmaxk τ wβ = c)
τnc wcτnc wc
nc c
(63)
Then

P r(ānc = ā|argmaxk
θ

ānk
ā
β = c) =θτnc wcτnc wcβ

−θ



!−θ−1

−Φn

e

ā
β
τnc wc

Φn

βθ −θ

θ
wcβθ .
= θā−θ−1 e−Φn τnc wc ā Φn τnc1
τnc wcβ(64)

Therefore,
P r(ānc ≤ ā|argmaxkānkθ w βθ ā−θ−Φn τncc.
β = c) = e
τnc wc(65)

Denote ι(ā) = P r(ānc = ā|argmaxk τ ānkwβ = c).
nccpSuppose that there are Lm
nc managers and Lnc workers that form production teams between

city n and city c, with n the origin city. For a team with managers productivity ā, herobjective function isā βl − wc l.
max f (Lmn)
lτnc
We get thatβf (Lmn )āτnc wcl(ā) =
1

γ

! 1

1−β

1

= κnc ā 1−β ,

1

− 1−β
1−β (τ
where κnc = β 1−β (Lm. The market clearing condition for low-skilled workers
nc wc )
n)
is
Z ∞
m
Lnc
ι(ā)l(ā)dā = Lpnc .
0That isθκnc θΦn τnc
wcβθ

Z ∞

θ

βθ −θ

0

Or
κnc θ

Z ∞

−θ

1

e−Φn τnc wc ā ā−θ−1+ 1−β dā =1e−y y −θ−1+ 1−β dy =

0

62

Lpnc
.
Lm
nc

1
Lpnc
θ
βθ − θ(1−β)
(Φ
τ
w
)
.
n
c
nc
Lm
nc

The total output is given by (up to a constant)
γ
1
(Lm
n)
θ
(1−β)
(Φn τncwcβθ ) θ (Lpnc )β (Lm
.
nc )
τnc
1

1

γ
θ
βθ θ β 1−βγθβθ θWe denote Snc (x, y) = (Lm, where (Lmn ) (Φn τnc wc ) x yn ) (Φn τnc wc ) is evaluated in
the scenario without the internet.

63

Additional Figures and Tables68log(population in 2013)
10
12
14

16

J

6

8

10
12
log(population in 1980)

14

16

Figure 9: log(population in 2013) against log(population in 1980) across CZs
Notes: Each dot represents a commuting zone. The linear correlation between log(labor supply in 2013)and log(labor supply in 1980) is 0.99.

64

Code
100
101
102
110
111
112
120
121
130
132
140
141
142
150
151
152
160
161
162
172
180
181
182
190
191
192
200
201
210
211
212
222
231
232
241
242

Industry Description
Meat products
Dairy products
Canned, frozen, and preserved fruits and vegetables
Grain mill products
Bakery products
Sugar and confectionery products
Beverage industries
Misc. food preparations and kindred products
Tobacco manufactures
Knitting mills
Dyeing and finishing textiles, except wool and knit goods
Carpets and rugs
Yarn, thread, and fabric mills
Miscellaneous textile mill products
Apparel and accessories, except knit
Miscellaneous fabricated textile products
Pulp, paper, and paperboard mills
Miscellaneous paper and pulp products
Paperboard containers and boxes
Printing, publishing, and allied industries, except newspapers
Plastics, synthetics, and resins
Drugs
Soaps and cosmetics
Paints, varnishes, and related products
Agricultural chemicals
Industrial and miscellaneous chemicals
Petroleum refining
Miscellaneous petroleum and coal products
Tires and inner tubes
Other rubber products, and plastics footwear and belting
Miscellaneous plastics products
Leather products, except footwear
Sawmills, planing mills, and millwork
Wood buildings and mobile homes
Miscellaneous wood products
Furniture and fixtures

Fort Index ∆ KM Index
0.111-0.013
0.142
0.048
0.194
0.097
0.171
0.156
0.082
-0.020
0.140
0.046
0.189
0.342
0.198
0.087
0.267
0.326
0.292
0.086
0.269
0.246
0.253
-0.019
0.274
0.221
0.212
N/A
0.272
0.098
0.228
0.125
0.239
0.146
0.362
0.148
0.362
0.042
0.322
0.108
0.263
0.030
0.324
1.070
0.325
0.328
0.223
0.321
0.126
0.291
0.196
0.373
0.155
0.110
0.155
0.453
0.257
0.122
0.257
0.123
0.231
0.089
0.276
0.181
0.117
0.120
0.224
0.146
0.239
N/A
0.650
0.097

Table 13: Change in KM Segregation Index and Fort (2017) Fragmentation Index

65

Code
250
251
252
261
262
270
271
272
280
281
282
290
291
300
310
311
312
320
321
322
331
340
341
342
351
352
360
361
362
370
371
372
381
390
391
610

Industry Description
Fort Index ∆ KM Index
Glass and glass products
0.238
0.156
Cement, concrete, gypsum, and plaster products
0.118
0.098
Structural clay products
0.192
0.195
Pottery and related products
0.192
0.191
Misc. nonmetallic mineral and stone products
0.137
0.097
Blast furnaces, steelworks, rolling and finishing mills
0.332
0.120
Iron and steel foundries
0.362
0.075
Primary aluminum industries
0.270
0.063
Other primary metal industries
0.272
0.096
Cutlery, handtools, and general hardware
0.378
0.244
Fabricated structural metal products
0.302
0.072
Screw machine products
0.352
N/A
Metal forgings and stampings
0.404
0.119
Miscellaneous fabricated metal products
0.318
0.164
Engines and turbines
0.501
0.450
Farm machinery and equipment
0.414
0.237
Construction and material handling machines
0.414
0.301
Metalworking machinery
0.409
0.233
Office and accounting machines
0.400
N/A
Computers and related equipment
0.501
1.833
Machinery, except electrical, n.e.c.
0.375
0.218
Household appliances
0.374
0.215
Radio, TV, and communication equipment
0.489
1.192
Electrical machinery, equipment, and supplies, n.e.c.
0.372
0.687
Motor vehicles and motor vehicle equipment
0.418
0.196
Aircraft and parts
0.500
0.494
Ship and boat building and repairing
0.228
0.163
Railroad locomotives and equipment
0.304
0.174
Guided missiles, space vehicles, and parts
0.500
0.845
Cycles and miscellaneous transportation equipment
0.466
0.337
Scientific and controlling instruments
0.467
0.793
Medical, dental, and optical instruments and supplies
0.278
0.440
Watches, clocks, and clockwork operated devices
0.467
N/A
Toys, amusement, and sporting goods
0.300
0.369
Miscellaneous manufacturing industries
0.300
0.194
Retail bakeries
0.082
0.088

Table 13 (continued). Change in KM Segregation Index and Fort (2017) Fragmentation Index
Notes: This table displays the change in the Kremer-Maskin (KM) skill segregation index
between 1980 and 2013 and the Fort (2017) fragmentation index in each industry (based on
1990 Census industry classification). We use industry concordance between census industry
classification and NAICS 4-digit available from the U.S. Census. When a Census industry
corresponds to multiple NAICS industries, we calculate the simple average of fragmentation
indices of the several NAICS industries.
66

Dependent variable: Change in high-skill employment share
(1)
(2)
(3)
(4)
high skilled defined bylog(labor supply in 1980)
state fixed effects
Observations
R2

67% cutoff
0.001
0.002∗∗(0.001) (0.0007)
No
Yes
722
722
0.003
0.298

80% cutoff
0.005∗∗∗ 0.006∗∗∗(0.0006) (0.0007)
No
Yes
722
722
0.112
0.372

(5)

(6)

college and above
0.004∗∗∗ 0.004∗∗∗(0.0007) (0.0006)
No
Yes
722
722
0.119
0.355

∗ p < 0.10, ∗∗ p < 0.05, ∗ ∗ ∗ p < 0.01

Table 14: Change in High-Skill Employment Share and City Size: Robustness Checks
Notes: Columns (1)-(2) define the high skilled as occupations whose rank is above 67% of all occupations in
1980. Columns (3)-(4) define the high skilled as occupations whose rank is above 80% of all occupations in
1980. Columns (5)-(6) define the high skilled as workers who have a college education or above. Columns(1), (3), and (5) leave out the state fixed effect and report the robust standard errors. Columns (2), (4),and (6) use the state fixed effect and report standard errors clustered at the state level.

67change in fraction of skilled 1980-2013
-.05
0
.05
.1
-.1
6

8

10

city size

12

14

16

Figure 10: Change in High-skill Employment Share with Respect to City Sizes
Notes: This figure displays the change in the skilled share from 1980 to 2013 against log of 1980 labor supply(raw data). High skill is defined as occupation rank above 75% using the 1980 mean of log hourly wage.

68

18
city size
45 degree line

City Size: Model

16

14

12

10

8

6
6

8

10

12

14

16

18

City Size: Data

Figure 11: City Size in 2013: Model v.s. Data
Notes: We solve our model using the calibrated parameter values. We then calculate the model-implied
equilibrium city sizes for each commuting zone and plot them against the actual log(labor supply in 2013).

69

20
15
predicted log(τ)
10
5
0
0

5

10

15

20

25

log(τ)

Figure 12: Fragmentation Cost Predicted by the Gravity Equation
Notes: This graph shows the predicted log(fragmentation cost τ ) implied by the gravity equation test with
the OLS estimation (controls are included) in Section 6. The x-axis is the data, and the y-axis is thepredicted value.

70