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Home / Publications / Research / Economic Brief / 2021

Economic Brief
October 2021, No. 21-34

How Do Firms Choose Where to Place Establishments?
Article by: Samira Gholami and Nicholas Trachter

This Economic Brief presents different considerations faced by firms when
organizing their operations across space. Following a recent research paper, it
explains why large firms tend to have a larger presence in high-density locations
than smaller firms, while the opposite is true in low-density locations.
How do firms decide where to set up locations? On one hand, it's costly to deliver goods to
customers, so firms may want to be as close to customers as possible. On the other hand,
concerns over cannibalization as well as the cost of managing a large amount of
establishments restrict how close the firm can get to its customers.
My (Nicholas) recent working paper "Plants in Space" — co-authored with Ezra Oberfield,
Esteban Rossi-Hansberg and Pierre-Daniel Sarte — finds that firms sort across space: Firms
with high productivity place more establishments in dense locations and fewer
establishments in low-density locations. Conversely, firms with low productivity place more
establishments in low-density locations and fewer in higher-density locations.
The paper provides examples of the way spatial characteristics affect firms' decisions. The
first example (Figure 1) shows Starbucks locations in Princeton, N.J., Richmond, Va., and
New York in 2014. Each square represents a 12-square-mile area.

We can see not only that the number of stores varies greatly across locations, but also that
the distance between stores in each location also greatly varies.
Another example comes from the distribution of Walgreens and Rite Aid stores in 2014.
Walgreens — the bigger (and presumably more productive) firm — has more
establishments than Rite Aid in areas with high population density, while Rite Aid has more
establishments than Walgreens in areas with low population density.

Modeling Optimal Firm Locations
The model in the paper covers consumers, developers and firms. In this article, we'll focus
on the problem of the firm, specifically where firms choose to locate.
Our model assumes that firms are heterogeneous in their innate productivity, but that
locations differ in their productivity advantage and the level of local demand, and that
shipping goods between two locations entails an "iceberg cost."1 Firms must also:
Choose how many establishments to open and where to locate them
Pay the commercial rental rate in each location where it opens an establishment
Decide how many workers to hire in each establishment
Decide which establishment will ship goods to each location to serve the local demand
Firms also face a span of control cost, where the effective productivity of the firm depends
negatively on the total number of establishments that the firm operates. This allows us to
capture the idea that it is more difficult to manage many establishments than a few of

Given the presence of iceberg costs, firms would like to set up multiple establishments to
be as close to demand as possible. But many establishments entail large setup and span of
control costs. These two costs — together with cannibalization concerns across the
establishments owned by the firm — counterbalance the strong incentives faced by the
firm to set up a multitude of production units across space.
Solving the problem of where firms should locate is complex. Namely, figuring out the level
of demand that an establishment will face entails figuring out the level of demand of all
other potential establishments owned by the firm. To address this issue, we use a limiting
case of the model economy, which preserves all the relevant elements and trade-offs in the
model discussed above. In the limit studied in the paper, the firm chooses a measure of
plants to open in each location, instead of making the individual decision of whether to
open an establishment in one point in space or not.

What Our Model Says
A strong implication of the model is that firms sort across space. Consider firms 1 and 2,
where firm 1 has higher productivity than firm 2. Theoretically, there's a cutoff rent where
firm 2 will place more establishments than firm 1 in locations below that rent, and firm 1
will place more establishments than firm 2 in locations above that rent.2
One important consideration is that firm 1 is also bigger than firm 2 and can place more
establishments: At a basic level, if it is optimal for firm 2 to place N2 establishments, firm 1
can always do better and thus N1 > N2. Similarly, because firm 1 is more productive, it will
hire more workers and, thus, be bigger. Finally, firm 1 also faces a higher marginal span of
control cost than firm 2 due to having more establishments.
When considering how many establishments to open in a location, firms attempt to equate
the gains from opening the establishments with the costs. The cost of opening an extra
establishment in a location is equal to the sum of the direct cost of opening the
establishment (measured by rent) and the firm's marginal span of control cost.
While firms 1 and 2 face the same rental cost at a location, firm 1 has a higher marginal
span of control cost as noted earlier. An implication is that firm 1 is less sensitive to rent
than firm 2. As a result, firm 1 places more establishments in high rent and high population
density locations than firm 2. The fact that firm 2 places more establishments than firm 1 in
low rent and low population density locations follows from span of control: High
productivity firms can economize on span of control costs by placing few plants, or no
plants, in these locations.
Empirical Evidence of Sorting

We test the sorting predictions using 2014 data from the National Establishment Time
Series (NETS) dataset that provides considerable information on firms:

All of their establishments' locations
Their level of employment
Their parent firm
While firm productivity is not observable, theory provides that it is possible to proxy
productivity with the firm employment level.
To study sorting, we portion the continental U.S. into squares with side length of M miles,
which allows us to study how firms set up their establishments across these squares. To
test the predictions, we focus on employment density.3
Is it the case that bigger, more productive firms sort towards high-density locations? To
study this, we compute for each firm the average employment density of the squares where
it places establishments. Each employment density in the average is weighted by the
number of establishments that the firm placed in each square. Then, because different
industries may have different configurations of plants across space, we remove an industry
fixed effect from the average computed for each firm.
Figure 2 below shows that, as predicted by the theory, there is a strong increasing
relationship between the size of the firm and the average employment density of locations
where the firm sets up its operations. And, as the figure shows, the result holds for
different sizes of the squares.

Do smaller firms place more establishments in low-density locations than bigger firms? One
way to study this empirically is to see whether the national size of the firm with the most
establishments in a location increases with the employment density of the location. If large
firms were to also dominate in low-density locations, we should see a flat profile instead of
an increasing profile.
Figure 3 presents this analysis, with industry fixed effects removed as was done previously.
As the figure shows, for all square sizes, the national size of the firm with most
establishments in a location increases with the employment density of the location.


This article shows that high-productivity firms place more establishments in high-density
locations than low productivity firms, and that the opposite is true in low density locations.
This result has interesting implications.
First, this sorting pattern helps to explain why some locations (counties, cities, etc.) are
more productive than others: Because high-productivity firms place more establishments in
high-density locations than low-productivity firms, high-density locations exhibit higher
productivity than low-density locations.
Second, the sorting pattern has important implications for what may happen after an
improvement in information and communication technologies, or ICT. Through the lens of
the model, an improvement in ICT reduces the span of control cost for firms. This cost
reduction induces highly productive firms to place more establishments in locations with
low population density, pushing lower-productivity firms to shrink their operations and, in
some cases, to exit the market.
Samira Gholami is a research analyst and Nicholas Trachter is a senior economist and
research advisor in the Research Department at the Federal Reserve Bank of Richmond.

1 An iceberg cost implies that if a unit of a good should arrive at location X from location Y, a

firm should ship more than one unit from Y. In other words, a fraction of the produced good
melts in the process of shipping it from Y to X.
2 Because, in equilibrium, rent is higher in denser locations, the result also implies that firms sort

in terms of population density.
3 This is used instead of the rental rate in a location due to data availability.

This article may be photocopied or reprinted in its entirety. Please credit the authors,
source, and the Federal Reserve Bank of Richmond and include the italicized statement
Views expressed in this article are those of the authors and not necessarily those of the Federal
Reserve Bank of Richmond or the Federal Reserve System.

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