# The Evolution of U.S. Retail Concentration††thanks:  This paper is
conditionally accepted at American Economic Journal: Macroeconomics. Any views
expressed are those of the authors and not those of the U.S. Census Bureau.
The Census Bureau’s Disclosure Review Board and Disclosure Avoidance Officers
have reviewed this information product for unauthorized disclosure of
confidential information and have approved the disclosure avoidance practices
applied to this release. This research was performed at a Federal Statistical
Research Data Center under FSRDC Project Numbers 1179 and 1975 (CBDRB-
FY19-P1179-R7207, CBDRB-FY20-P1975-R8604 and CBDRB-FY23-P1975-R10585).
We gratefully acknowledge advice from Thomas Holmes, Teresa Fort, Amil Petrin,
Joel Waldfogel, Emek Basker, Brian Adams, Fatih Guvenen, Juan Herreño,
Gueorgui Kambourov, Burhan Kuruscu, Rory McGee, Emily Moschini, Martin
O’Connell, Jane Olmstead-Rumsey, Pascual Restrepo, Jeff Thurk, and Nicholas
Trachter. We are also indebted to an anonymous referee for constructive
comments. We also thank participants of seminars at various institutions as
well as participants at the 2021 NBER SI CRIW, 2021 CEA, 2021 IIOC, and 2019
SED meetings and the 2018 FSRDC conference. This paper is based upon work
supported by the Doctoral Dissertation Fellowship at the University of
Minnesota.

Dominic A. Smith
Bureau of Labor Statistics Email<EMAIL_ADDRESS>Web:
https://www.bls.gov/pir/authors/smith.htm. Sergio Ocampo
University of Western Ontario Email<EMAIL_ADDRESS>Web:
https://sites.google.com/site/sergiocampod/.

###### Abstract

Increases in national concentration have been a salient feature of industry
dynamics in the U.S. and have contributed to concerns about increasing market
power. Yet, local trends may be more informative about market power,
particularly in the retail sector where consumers have traditionally shopped
at nearby stores. We find that local concentration has increased almost in
parallel with national concentration using novel Census data on product-level
revenue for all U.S. retail stores between 1992 and 2012. The increases in
concentration are broad based, affecting most markets, products, and retail
industries. We show that the expansion of multi-market firms into new markets
explains most of the increase in national retail concentration, with
consolidation via increases in local market shares increasing in importance
between 1997 and 2007, and single-market firms playing a negligible role.
Finally, we find that increases in local concentration can explain one-quarter
to one-third of the observed rise in retail gross margins.

JEL: D4, L8, R1

Keywords: Retail, Local Markets, Concentration, Herfindahl-Hirschman Index

###  1 Introduction

There is an economy-wide trend toward greater ownership concentration and an
increase in the dominance of large, established firms. These trends have been
accompanied by rising markups, which raises concerns about increasing market
power.111 See Autor, Dorn, Katz, Patterson, and Van Reenen ((2020) for
evidence of increased concentration in retail and other sectors, and Decker,
Haltiwanger, Jarmin, and Miranda ((2014, 2020) for the dominance of large
firms. De Loecker, Eeckhout, and Unger ((2020) and Hall ((2018) document
increasing markups.  The increase in concentration has been particularly
strong in the retail sector, which accounts for 11 percent of U.S. employment
and 6 percent of U.S. GDP. Both the share of sales going to the largest firms
and the national Herfindahl-Hirschman Index (HHI) have been increasing for
decades across retail industries ((Autor, Dorn, Katz, Patterson, and Van
Reenen, 2020; Hortaçsu and Syverson, 2015). These changes potentially reflect
a decrease in retail competition.

However, local concentration is more informative than national concentration
about the degree of competition and the evolution of retail markups, because
consumers in the retail sector primarily choose among local stores. Retail
firms also compete within and across industries, as firms from different
industries often sell identical products. This raises the need for new
measures of retail firm concentration that reflect the evolution of local
retail markets at the product and industry levels.

In this paper, we use novel U.S. Census data covering all retail
establishments to show that both national and local firm concentration have
increased. The data come from the Census of Retail Trade (CRT) and span 1992
to 2012, allowing us to measure changes in local and national concentration
over 20 years. Our data allow us not only to measure industry-based
concentration, but also to construct sales by product for individual retail
stores with which we compute new measures of concentration for local product
markets, handling retailers that sell multiple products by assigning their
sales to the appropriate markets. We consistently find increases across these
measures.

Our data show that the national and local HHI increased almost in parallel
between 1992 and 2012. We show that the HHI measures the probability that two
dollars spent at random are spent at the same firm. We use this fact to
interpret changes in the HHI. The national product HHI increased from 1.3 to
4.3 between 1992 and 2012, indicating that the probability that two random
dollars spent on a product anywhere in the U.S. are spent at the same firm has
increased by 3 percentage points. Local (commuting zone) concentration in
product markets increased by 2.2 percentage points, from 6.4 to 8.6. Moreover,
we find that the increases in local retail concentration hold and are often
larger when looking at an extended sample dating back to 1982, when changing
the geographical definition of local markets, or when concentration is
measured using the sales share of the largest firms.

We find that the increases in local concentration were widespread, with a
majority of markets and product categories experiencing increasing
concentration. The local HHI increased in 72 percent of commuting zones
between 1992 and 2012, with markets with increasing concentration accounting
for 66 percent of retail sales in 2012. Moreover, the increases in
concentration were substantial, with 40 percent of markets presenting
increases of more than 5 percentage points (well above the thresholds in the
merger guidelines of the Department of Justice and Federal Trade Commission,
2010). Concentration also increased for seven of the eight major product
categories in retail between 1992 and 2012, with Clothing being the
exception.222 The eight major product categories are Clothing, Furniture,
Sporting Goods, Electronics & Appliances, Health Goods, Toys, Home Goods, and
Groceries. These categories account for 94 percent of retail sales. For
comparison, the eight largest (out of 61) six-digit NAICS codes in retail
account for two-thirds of sales.

We examine how online and other non-store retailers affect local concentration
and find they have a small effect because they account for less than 10
percent of CRT sales throughout our sample. Establishing the exact effect of
non-store retailers on local concentration is challenging because the CRT does
not contain the location of sales for non-store retailers. Nevertheless, we
obtain bounds for the effect of non-store retailers by assigning their
national sales to local markets using a range of assumptions on how
concentrated their local sales are. Including non-store retailers implies
smaller increases in national and local concentration under most assumptions.

We also measure local and national retail concentration in six-digit NAICS
industries and compare them to our product-based results. We find that
industry-based measures exhibit a stronger increase in concentration than
product-based measures. Commuting zone concentration increased by 12.6
percentage points between 1992 and 2012, an increase six times greater than
the increase in local product concentration. Local concentration increased
within all eight three-digit NAICS subsectors, led by a 28 percentage point
increase in the industries that make up the General Merchandising subsector.

The main difference between product- and industry-based measures of
concentration is the type of competition that they emphasize. Product-based
measures emphasize competition in the sale of goods, while industry-based
measures emphasize competition in retail services. This difference is made
clear in the treatment of general merchandisers and other multi-product
retailers, which, by definition, sell the same products as retailers in other
industries, but offer a different service precisely by offering a wider range
of products.333 For example, Walmart is in the general merchandising subsector
(three-digit NAICS 452) but competes with grocery, clothing, and toy stores.
However, a retailer in a clothing industry is likely to carry a large number
of clothing items, while a general merchandiser like Walmart carries other
products in addition to a smaller selection of clothing. Walmart reports SIC
code 5331 to the Security and Exchange Commission, which corresponds to NAICS
452990 ((Securities and Exchange Commission, 2020). References to specific
firms are based on public information and do not imply the company is present
in the confidential data.  In fact, general merchandisers account for more
than 20 percent of sales in Electronics & Appliances, Groceries, and Clothing,
and their expansion has been linked to the closure of grocery stores
((Arcidiacono, Bayer, Blevins, and Ellickson, 2016), showing that competition
across industries is a relevant feature of retail markets. The same pattern
arises in more detailed industries, as we show in Section 2 and Appendix C.

Having established the increase in both national and local retail
concentration, we investigate the relationship between these two trends. We
find that the two trends are linked by the expansion and consolidation of
multi-market retailers, with the expansion of large retailers across markets
accounting for 89 percent of the increase in national retail concentration
between 1992 and 2012. In this way, concentration has increased as consumers
in different markets increasingly buy from the same firms, adding to the
findings of previous papers such as Cao, Hyatt, Mukoyama, and Sager ((2019),
Hsieh and Rossi-Hansberg ((2023), and Rossi-Hansberg, Sarte, and Trachter
((2021) on the role of the expansion of large firms in explaining changes in
the U.S. economy.444 The expansion of large retail firms has led to the
closing of small stores ((Jia, 2008; Haltiwanger, Jarmin, and Krizan, 2010)
and grocery chains ((Arcidiacono et al., 2016), as well as higher retail
employment in local labor markets ((Basker, 2005) and increased welfare for
consumers ((Leung and Li, 2022, 2023).

Our findings also reveal that single-market firms operating in local product
markets have a negligible effect in the evolution of national concentration.
This is because the distribution of retail sales across locations in the U.S.
implies that even the largest retail markets in the U.S. are too small to
affect national trends. By contrast, the national market share of retail firms
present in at least 50 commuting zones increased from 34 to 58 percent between
1992 and 2012, despite there being fewer than 350 of these firms in the U.S.
(or less than 0.1 percent of retail firms). All this while their average local
market share barely increased from 3.2 to 3.4 percent.

We end the paper with a discussion of the implications of our findings. Under
Cournot competition there is a direct link between local concentration and
firms’ margins. This link implies increases in retailers’ margins of 1.6
percentage points from the overall increase in local product market
concentration. Taking into account differences in concentration trends and
retailers’ margins across products increases the estimate to 2.1 percentage
points.555 Many of the concerns about concentration leading to higher markups
(Hall, 2018; Traina, 2018; Edmond, Midrigan, and Xu, 2019; De Loecker et al.,
2020) would operate through local markets, particularly in labor and retail
markets. For instance, higher local employment concentration has been shown to
negatively impact wages ((Jarosch, Nimczik, and Sorkin, 2020; Azar, Berry, and
Marinescu, 2019; Rinz, 2020; Berger, Herkenhoff, and Mongey, 2022), and has
been associated with the presence of large publicly traded firms that are
increasingly owned by common investors ((Azar, Qiu, and Sojourner, 2022).
These changes in margins are meaningful, accounting for one-fourth to one-
third of the 6.0 percentage points increase in retailers gross margins between
1993 and 2012 from the Annual Retail Trade Survey (ARTS). We also discuss the
importance of multi-market pricing and the growth of online retailers. These
trends imply that retailers may increasingly set prices based on their average
market power across markets, attenuating the impacts of increasing local
concentration on retailer margins.

##### Comparison to Previous Concentration Results

Our finding of parallel increases in local and national concentration
complements work documenting increasing concentration across the U.S.
economy.666 See Basker, Klimek, and Van ((2012); Foster, Haltiwanger, Klimek,
Krizan, and Ohlmacher ((2016); Hortaçsu and Syverson ((2015); Grullon, Larkin,
and Michaely ((2019); Ganapati ((2021).  In particular, our product-based
measures complement work finding increasing national concentration at the
industry level using the Census of Retail Trade ((Autor et al., 2020). The
increases in local concentration in the retail sector that we document are in
line with the findings of Rinz ((2020) and Lipsius ((2018), who study local
labor markets using the Longitudinal Business Database (LBD), another U.S.
Census dataset, and contrast with the decreasing trends in local concentration
that they and Rossi-Hansberg et al. ((2021) find outside of retail. We provide
more evidence that retail is the only sector with consistently increasing
local concentration.

We provide new series of concentration by product categories, which better
reflect the nature of competition in retail, as well as series by industry at
different levels of geographic aggregation. Our results differ from the
industry-based results in Rossi-Hansberg et al. ((2021) and studies of
consumer purchasing decisions by Neiman and Vavra ((2020) and Benkard,
Yurukoglu, and Zhang ((2021), that find decreasing concentration.

Rossi-Hansberg et al. ((2021) base their results on data from the National
Establishment Time Series (NETS), a private dataset, that does not contain
sales by product categories, preventing them from addressing cross-industry
competition. Moreover, the NETS includes restaurants in the retail sector
while the CRT does not, which explains part of the difference between the two
studies ((Trachter, 2021).777 The NETS also has issues tracking establishments
and imputing sales of retailers ((see, Crane and Decker, 2020; Decker, 2020).
There are also methodological differences between our studies. We consider a
range of methods to calculate the local HHI to make our studies more
comparable. We find increases in local concentration with all but one, with
changes in local industry concentration between -1.5 and 12.6 percentage
points. The baseline estimate in Rossi-Hansberg et al. that local retail
concentration decreased by 17 percentage points falls significantly outside
this range. Half of the remaining difference is due to data source as we show
in Section 3.4 and Appendix E.

On the other hand, Benkard et al. ((2021) study the ownership of the brands of
goods and services that consumers purchase, finding that both national and
local concentration among the producers of these products decrease over time,
while Neiman and Vavra ((2020) use scanner data to show that aggregate
concentration in household UPC purchases of groceries has fallen. We calculate
firm-level concentration among the retailers that sell those (and other) goods
using data covering all retail sales. Taken together, our results are
complementary as they speak to different aspects of the retail sector. On
aggregate, consumers are simultaneously purchasing a wider variety of brands
as they buy those products from a smaller set of retail firms. In this way,
increasing retail concentration could cause retail firms to have both more
market power with consumers and better negotiating power with suppliers.

Finally, we show how the consolidation and expansion of single- and multi-
market firms has shaped the relationship between local and national
concentration trends. Our results extend previous work documenting the
expansion of individual retail firms ((Basker, 2005, 2007; Holmes, 2011) and
national chains ((Miranda, Klimek, and Jarmin, 2004; Foster, Haltiwanger, and
Krizan, 2006; Foster, Haltiwanger, Klimek, Krizan, and Ohlmacher, 2016) in the
1980s and 1990s. We further contribute by showing that this expansion was
followed by within consolidation of large retailers that explains 40 percent
of the increase in national concentration between 1997 and 2007.

The rest of the paper proceeds as follows. Section 2 describes the data and
how we construct store-level sales by product. Section 3 measures retail
concentration and documents its evolution. Section 4 decomposes national
concentration into local and cross-market concentration. Section 5 discusses
implications for retailers’ market power.

###  2 Data: Retailer Revenue for All U.S. Stores

This section describes the creation of new data on store-level revenue for 18
product categories for all stores with at least one employee in the U.S.
retail sector. These data allow us to construct detailed measures of
concentration that take into account competition between stores selling
similar products in specific geographical areas.

####  2.1 Data Description

We use confidential U.S. Census Bureau microdata that cover 1992 to 2012
((U.S. Census Bureau, 1992-2012). The data source is the Census of Retail
Trade (CRT), which provides revenue by product type for retail stores
(establishments) in years ending in 2 and 7. We compile CRT data on product-
level revenue and information on each store’s location to define which stores
compete with each other. Importantly, a store’s local competition will include
stores in many different industries inside the retail sector because stores of
different industries can sell similar products. This is particularly relevant
for stores in the general merchandising subsector, but it also affects stores
across more detailed industries (e.g., family clothing stores, women’s
clothing stores, and men’s clothing stores). The data we create here are
uniquely equipped to deal with cross-industry competition.

We combine the CRT data with the Longitudinal Business Database (LBD) ((Jarmin
and Miranda, 2002), which contains data on each store’s employment and allows
us to track stores over time. The LBD’s firm identifiers allow us to determine
which stores are owned or controlled by the same entity.888 See
https://www.census.gov/econ/esp/definitions.html This definition of firms
combines stores with different names if they are subsidiaries of the same
firm. It also combines the stores of entities that merge into one firm.999 The
effect of mergers on concentration depends on whether the stores that merge
sell the same products, are in the same industries, and are located in the
same geographical markets.  We calculate all concentration measures at the
firm level by combining store sales of a firm in each market.

####  2.2 Sample Construction

The retail sector is defined based on the North American Industrial
Classification System (NAICS) as stores with a two-digit code of 44 or 45. As
such, it includes stores that sell final goods to consumers without performing
any transformation of materials. We use the NAICS codes available from the CRT
as the industry of each store. The sample includes all stores with positive
sales and valid geographic information that appear in official CRT and County
Business Patterns (CBP) statistics that sell one of the product categories
used in this study.101010 We exclude sales of gasoline and other fuels, autos
and automotive parts, and non-retail products because franchising makes it
difficult to identify firms. In our main results we exclude non-store
retailers because sales from these stores are typically shipped to different
markets than their physical location. We explore the implications of this
assumption in Section 3.3.

Table 1 shows summary statistics for our sample. Even though the number of
establishments and firms fluctuates over time, there is an overall decrease in
both counts between 1992 and 2012. Notably, the decrease in firms is double
the decrease of establishments. This trend is consistent with the growing
importance of multi-market firms in rising cross-market concentration that we
show in Section 4. Despite these trends, employment increases over time,
representing about 9 percent of nonfarm U.S. employment over the whole sample
period.111111 U.S. employment numbers come from Total Nonfarm Employees in the
Current Employment Statistics ((Bureau of Labor Statistics, 2019).

Table 1: Sample Summary Statistics

| 1992 | 1997 | 2002 | 2007 | 2012
---|---|---|---|---|---
Establishments | 908 | 942 | 913 | 912 | 877
Firms | 593 | 605 | 589 | 566 | 523
Sales | 1,004 | 1,368 | 1,657 | 2,062 | 2,195
Employment | 9.91 | 11.60 | 11.89 | 12.78 | 12.31

  * •

Notes: Establishment and firm numbers are expressed in thousands. Sales and
employment numbers are expressed in millions. The numbers are based on
calculations from the Census of Retail Trade and the Longitudinal Business
Database. (CBDRB-FY20-P1975-R8604)

####  2.3 Creation of Product-Level Revenue

We construct product-level revenue data for all U.S. stores, allowing us to
assign a store in a given location to markets based on the types of products
it carries. To do this, we exploit the CRT’s store-level data on revenue by
product line (e.g., men’s footwear, women’s pants, diamond jewelry). We then
aggregate product line codes into 18 categories such that stores in industries
outside of general merchandise and non-store retailers sell primarily one type
of product.121212 Table B.2 lists all the product categories. Unless otherwise
stated, we use data from all products for our aggregate results. In Section
3.2 we focus on the eight “main” product categories that account for 94
percent of store sales in our sample for results for individual product
categories. The remaining categories are individually small and have not been
released due to disclosure limitations.  For instance, stores in industries
beginning with 448 (clothing and clothing accessory stores) primarily report
sales in products such as women’s dress pants, men’s suits, and footwear,
which are grouped into a Clothing category.

The product-level data we construct opens up the possibility to study product
markets covering all of retail. Alternative data sources, such as the
NielsenIQ Homescan Consumer Panel and the Nielsen Scanner Data, provide more
detailed product descriptions but lack the representativeness of our sample,
focusing mostly on grocery and health products for a limited sample of people
or retailers, making them less useful for computing concentration at the firm
level.131313 Firm level concentration is the relevant measure of concentration
for antitrust in retail. However, detailed product concentration is
informative about consumer behavior and retailers upstream market power with
their suppliers ((Benkard et al., 2021; Neiman and Vavra, 2020).  Our
definition of product categories implies slightly higher levels of aggregation
than six-digit NAICS industry codes while dealing with cross-industry
competition (see Appendix C). It also addresses the fact that several product
lines are consistently sold together, as is the case for men’s wear (product
line code—plc—20200), women’s juniors’ and misses’ wear (plc 20220), and
footwear products (pcl 20260), or for major household appliances (plc 20300)
and TVs (plc 20320).

Aggregating product lines into categories allows us to accurately impute
revenue by category for stores that do not report product-level data. The CRT
asks for sales by product lines from all stores of large firms and a sample of
stores of small firms. For the remainder, store-level revenue estimates are
constructed from administrative data using store characteristics (e.g.,
industry and multi-unit status). These revenue estimates are constructed for
stores that account for about 20 percent of sales in each year. Appendix B
provides the details of this procedure.

Our product-level revenue data also accounts for the presence of multi-product
stores. When a store sells products in more than one category, we assign the
store’s sales in each category to its respective product market. Consequently,
a given store faces competition from stores in other industries. For example,
an identical box of cereal can be purchased from Walmart (NAICS 452), the
local grocery store (NAICS 448), or online (NAICS 454).141414 The authors
found a 10.8 oz box of Honey Nut Cheerios at Walmart, Giant Eagle, and
Amazon.com on June 22, 2020.

Table 2 shows that cross-industry competition is pervasive in retail. On
average, the main subsector for each product accounts for just over half of
the product’s sales. The remaining sales are accounted for by multi-product
stores, particularly from the general merchandise and non-store retailer
industries, which are included in the appropriate product markets based on
their reported sales. The high sales shares of these multi-product stores
makes industry classifications problematic when studying competition. Table
D.1 reports the composition of sales for each product category, further
distinguishing between general merchandisers and other multi-product
retailers.

Moreover, even stores in detailed industries (six-digit NAICS) sell the same
products. For example, men’s clothes are available at Men’s clothing stores
(448110), and family clothing stores (448140), in addition to department
stores (452111) and discount department stores (452112), see Table C.4 in
Appendix C. Although the shopping experience may differ between stores in
different industries a consumer looking to buy a new pair of jeans might
consider stores in more than four different NAICS industries.

Table 2: Share of Product Category Sales by Main Subsector

| 1992 | 2002 | 2012
---|---|---|---
Avg. Main Subsector Share | 55.8 | 53.2 | 50.0
Max Main Subsector Share | 79.8 | 73.1 | 72.4
Min Main Subsector Share | 30.3 | 27.6 | 22.0

  * •

Notes: The numbers are based on calculations from the Census of Retail Trade.
The average is the arithmetic mean across the eight main product categories of
the share of sales accounted by establishments in the product’s associated
subsector. Shares are multiplied by 100.

####  2.4 Definition of Local Markets

We use the 722 commuting zones that partition the contiguous U.S. as our
definition of local markets. Commuting zones are defined by the U.S.
Department of Agriculture such that the majority of individuals work and live
inside the same zone, and they provide a good approximation for the retail
markets in which stores compete. If individuals live and work in a commuting
zone, they likely do most of their shopping in that region.

Our results regarding the increasing trends in local concentration and the
role of local trends for national concentration are robust to changes in the
definition of retail markets. Choosing a larger geographical unit when
defining retail markets, such as commuting zones, typically increases the
contribution of local concentration to national concentration relative to
smaller geographical units such as counties or zip codes. Larger geographical
units also tend to have lower levels of concentration than smaller units.
However, despite differences in levels of concentration, measures at the zip
code, county, commuting zone, and Metropolitan Statistical Area (MSA) levels
lead to the same conclusions about the trend in local concentration, even in
an extended sample dating back to 1982 (see Appendix D.2).

###  3 Changes in Retail Concentration

In this section, we use the detailed microdata described in Section 2 to
measure national and local concentration in the U.S. retail sector. We find
that local concentration has increased almost in parallel with national
concentration. The increases in concentration are broad based, affecting most
markets, product categories, and retail industries.

Our primary measure of concentration is the firm Herfindahl-Hirschman Index
(HHI) for a given product category. We denote by $i$ an individual firm and by
$j$ a product so that $s_{i}^{jt}$ represents the sales share of firm $i$ in
product $j$ at time $t$. More generally, we define subscripts and superscripts
such that $s_{a}^{b}$ is the share OF $a$ IN $b$. The national HHI in a year
is defined as the sum of the product-level HHIs weighted by the share of
product $j$’s sales in total retail sales, $s_{j}^{t}$:

$\displaystyle
HHI^{t}=\sum_{j=1}^{J}s_{j}^{t}HHI_{j}^{t},\quad\text{with}\quad
HHI_{j}^{t}=\sum_{i=1}^{N}\left(s_{i}^{jt}\right)^{2},$ (1)

while the HHI of location $\ell$ and product $j$ in year $t$ is calculated as

$\displaystyle HHI_{\ell j}^{t}=\sum_{i=1}^{N}\left(s_{i}^{j\ell
t}\right)^{2}.$ (2)

The HHI for product $j$ measures the probability that two dollars, $x$ and
$y$, chosen at random, are spent at the same firm. This probabilistic
interpretation of the HHI provides a direct way to understand its level and
changes.

Figure 1 plots national and local concentration in the U.S. retail sector as
measured by the HHI. Between 1992 and 2012, both national and local
concentration increased at a similar pace. National concentration more than
tripled from 0.013 to 0.043. That is, the probability that two dollars are
spent in the same firm in the U.S. goes from 1.3 percent in 1992 to 4.3
percent in 2012. Local concentration, measured by the commuting zone HHI,
increased by 34 percent from 6.4 percent to 8.6 percent, a similar increase to
that of the national HHI.

Figure 1: National and Local Concentration Notes: The numbers are based on
calculations from the Census of Retail Trade. The figure plots the Herfindahl-
Hirschman Index (HHI) for local markets defined at the commuting zone level
and national concentration. The local HHI is aggregated using each location’s
share of national sales within a product category. The numbers are sales-
weighted averages of the corresponding HHI across product categories. (CBDRB-
FY20-P1975-R8604)

We extend these results back to 1982 and consider additional measures of local
concentration measures at the zip code, county, and MSA level (Appendix D.2).
We find no change in the increasing trends for national and local
concentration. Most of this increase occurred between 1997 and 2007, after
which all concentration measures plateau. In fact, the national HHI was low
and grew at a low rate before 1997. National concentration increased by 1
percentage point in the 15 years between 1982 and 1997; by contrast, it
increased 2.3 percentage points in the 10 years between 1997 and 2007. We also
show that increases in local concentration are found with other definitions of
local markets and that these changes are broad based across products and
geographic areas.

The national concentration results are consistent with previous industry-level
work using sales and employment for various sectors, including retail ((Basker
et al., 2012; Foster et al., 2016; Lipsius, 2018; Autor et al., 2020; Rinz,
2020; Rossi-Hansberg et al., 2021). The local concentration results are also
consistent with studies on labor market concentration that find increasing
local concentration in retail but decreasing local concentration in other
sectors ((Rinz, 2020; Lipsius, 2018). We show that industry-based measures of
sales concentration also rise at both the national and local level in Section
3.4 and contrast these results with those of Rossi-Hansberg et al. ((2021) who
report decreasing local concentration.

####  3.1 Changes in Concentration across Markets

We now turn to the distribution of changes in concentration across markets. We
find that the increases in concentration have been broad based. Sixty-six
percent of dollars spent in 2012 are spent in markets that have increased
concentration since 1992 (Figure 2(a)). In 20 years, 40 percent of markets
accounting for 17 percent of spending have increases in concentration of over
5 percentage points (Figure 2(b)). These changes are significant. For
comparison, the Department of Justice considers a 2 percentage point increase
in the local HHI potential grounds for challenging a proposed merger
((Department of Justice and Federal Trade Commission, 2010). On the other
side, only 12 percent of markets accounting for 2 percent of spending
experienced decreases in the local HHI at at least 5 percentage points.

Even though local retail concentration has sustainably increased between 1992
and 2012, the changes in concentration were more widespread between 1992 and
2002, when concentration increased in almost 70 percent of markets. The share
of markets with increasing concentration was lower in the following decade
with just under 60 percent of markets increasing their concentration. We
explore these patterns in in Appendix D.5 where we present changes in
concentration by decade.

Figure 2: Changes in Concentration across Markets

(a) Weighted 1992–2012

(b) Unweighted 1992–2012

Notes: The numbers are based on calculations from the Census of Retail Trade.
The left panel weights markets by the average value of sales in the market in
1992 and 2012. The right panel shows the fraction of markets, commuting
zone/product category pairs, with changes in concentration of a given size.
(CBDRB-FY23-P1975-R10585)

####  3.2 Changes in Concentration across Products

Between 1992 and 2012, both local and national concentration increased for
seven of the eight major product categories, Clothing being the exception.
Figure 3(a) shows that these increases were large for many products. Six of
the eight categories had an increase in HHI between 3 and 4 percentage points.
Despite this common trend, the changes in concentration vary substantially
across product categories. Local concentration in Groceries increased by only
1.1 percentage points and decreased in Clothing by 2012, while it almost
doubled in Home Goods and Electronics & Appliances.

Figure 3(b) shows the levels of national concentration for each product
category between 1992 and 2012. The increases in national concentration are
widespread and significant. Six of the categories have larger absolute changes
in national concentration relative to local concentration even though the
levels of national concentration are markedly lower than those of local
concentration.

Figure 3: Local and National Concentration across Product Categories

(a) Local Concentration

(b) National Concentration

Notes: The numbers are national and local Herfindahl-Hirschman Indexes (HHI)
by product weighted by market size from the Census of Retail Trade microdata.
(CBDRB-FY20-P1975-R8604)

Finally, comparing Figures 3(a) and 3(b) shows that not all product markets
evolved in the same way between 1992 and 2012. The markets for Furniture and
Clothing changed very little, and both have relatively low levels of both
local and national concentration. On the other hand, local markets for
Groceries and Health Goods became slightly more concentrated, while at the
national level, concentration has increased more than fourfold.

####  3.3 Impact of Online and Other Non-Store Retailers

The previous results calculated local concentration using only brick-and-
mortar retailers. In what follows, we consider the potential impact of online
and other non-store retailers on local concentration. The market share of non-
store retailers has more than tripled between 1992 and 2012. However, the
overall importance of non-store retailers remained limited through 2012. The
initial sales share of non-store retailers is low, just 2.7 percent in 1992.
This low share reflects both the absence of online retailers and the limited
role of other retailers that rely on mail order and telephone sales. The sales
share of non-store retailers had risen to 9.5 percent by 2012, driven by an
increase in online sales. The increase was uneven across product categories.
Non-store retailers had significant market share in product categories, such
as Furniture, Clothing, and Sporting Goods, but have almost no market share in
Groceries and Home Goods (see Appendix D.3).

The effect of online and other non-store retailers on local concentration
depends on how their sales are distributed across and within markets.
Unfortunately, the CRT does not record the location in which non-store
retailers sell their products, making it impossible to determine the exact
effect of these retailers on local concentration. Nevertheless, we can
generate bounds for the effect of non-store retailers while being consistent
with their behavior at the national level. To do this, we assume that the
share of retail spending that goes to non-store retailers is constant across
markets within a product category and is equal to the national sales share of
non-store retailers in that category.151515 It is possible for brick-and-
mortar retailers to sell online becoming mixed channel retail firms. The CRT
assigns these transactions to the establishment that fulfills them.
Transactions shipped from a brick and mortar establishment are typically
included in the sales of that establishment and are thus already accounted for
in our concentration calculations. Transactions shipped from a dedicated
fulfillment center are assigned to an establishment of the same firm in a non-
store retailer industry. We have studied multiple ways of assigning the sales
of mixed channel retailers and found that they have limited effects through
2012 because their sales are relatively low.

Having distributed the sales of non-store retailers across markets, we can
construct a lower and upper bound for the local HHI. The total effect on
concentration depends on the total market share of non-store retailers and how
concentrated they are. The lower bound assumes that non-store retailers are
atomistic, with the sales share of each non-store retailer equal to zero. The
lower bound is

$\displaystyle\underline{HHI}=\left(1-s_{NS}\right)^{2}HHI_{BM},$ (3)

where $s_{NS}$ corresponds to the sales share of non-store retailers and
$HHI_{BM}$ to the HHI of brick-and-mortar stores. In this case, non-store
retailers decrease concentration by reducing the sales share of brick-and-
mortar stores. The size of this decrease depends on the sales shares of non-
store retailers in the product category. The upper bound assumes that all the
sales of non-store retailers belong to a single stand-in firm. The upper bound
is

$\displaystyle\overline{HHI}=\left(1-s_{NS}\right)^{2}HHI_{BM}+s_{NS}^{2}.$
(4)

This is an upper bound on concentration under the assumption that firms do not
have both brick-and-mortar and non-store establishments, which is consistent
with the data.

Figure 4 shows the bounds we construct for local concentration across product
categories in the retail sector. As expected, including non-store retailers
for categories like Home Goods or Groceries hardly affects the level of
concentration because the market share of non-store retailers remains low
throughout. The effects are larger for the other categories, especially for
2012. Accounting for non-store retailers reduces concentration in most
categories because of the decrease in market share among brick-and-mortar
stores. For most product categories, the bounds for local concentration lie
below the estimated HHI for brick-and-mortar stores (marked by the diamonds in
the figure). It is only in Electronics & Appliances, and to a lesser extent in
Clothing, that the market share of non-store retailers is large enough for
their inclusion to potentially increase concentration.

When non-store retailers are included, there is still a clear increase in
local concentration between 1992 and 2002, although the levels are slightly
lower. Moving from 2002 to 2012, the story becomes ambiguous, especially for
product categories with a significant share of their sales going to non-store
retailers. In many cases, the bounds for 2012 contain the bounds for 2002,
indicating local concentration could either be increasing or decreasing
depending on the concentration among non-store sales. At a national level,
non-store retailers were not highly concentrated during this time period
((Hortaçsu and Syverson, 2015), and thus the increasing importance of non-
store retailers is potentially limiting the increase in local market
concentration between 2002 and 2012. In Table D.2 of Appendix D.3, we show
that national concentration is unaffected by non-store retailers until 2002
and does reduce its increase afterwards.

Figure 4: Local Concentration and Non-Store Retailers Notes: The numbers are
based on calculations from the Census of Retail Trade. Diamonds mark local
concentration for brick-and-mortar stores as measured by the Herfindahl-
Hirschman Index (HHI) at the commuting zone level. The continuous lines cover
the bounds on concentration including non-store retailers. We assume that
sales of non-store retailers are distributed across local markets
proportionately to the sales of brick-and-mortar retailers. The upper bound
assigns all the sales of non-store retailers to a single stand-in firm. The
lower bound assumes that non-store retailers are atomistic, with the sales
share of each individual non-store retailer equal to zero. (CBDRB-
FY20-P1975-R8604)

####  3.4 Comparing Industry- and Product-Based Results

We now document the evolution of industry-based concentration measures. These
measures capture the variation in retail services offered by different
industries. For instance, general merchandisers offer a variety of products,
and consumers value the ability to buy multiple products in one location
((Seo, 2019). In this sense, industry based measures focus on a different
dimension of competition between retail stores than the product-based measures
we have presented.

We find larger increases in both national and local concentration at the
industry level than at the product level. We study industry-based measures of
concentration defined at the six-digit NAICS level, the most disaggregated
industries available in the data. We aggregate these results to the three-
digit NAICS level using a sales-weighted average. Table 3 shows that national
industry-based concentration increases by 8.7 percentage points, 5.7
percentage points more than with product-based measures. Commuting zone
concentration goes up by 12.6 percentage points between 1992 and 2012 when
measured at the industry level, 10.4 percentage points more than the product-
based measure. The same patterns arise when defining markets at the zip code
level and show that the large increase in industry-based local concentration
is not a feature of the geographical aggregation of markets.

A significant portion of the increase in industry concentration comes from
six-digit industries within the general merchandise subsector (NAICS 452),
where local concentration increased by 28.2 percentage points (see Figure D.5
in Appendix D.6). This change is at least partially due to general
merchandisers selling an increasing number of products and may not reflect
increasing market power.

Table 3: Comparison of Product- and Industry-Based Concentration

| National Concentration
---|---
| 1992 | 1997 | 2002 | 2007 | 2012
Product Based | 0.013 | 0.018 | 0.031 | 0.042 | 0.043
Industry Based | 0.029 | 0.046 | 0.085 | 0.105 | 0.116
| Commuting Zone Concentration
Product Based | 0.064 | 0.065 | 0.077 | 0.086 | 0.085
Industry Based | 0.177 | 0.199 | 0.263 | 0.287 | 0.302
| Zip Code Concentration
Product Based | 0.264 | 0.277 | 0.288 | 0.286 | 0.277
Industry Based | 0.530 | 0.552 | 0.602 | 0.611 | 0.615

  * •

Notes: The numbers come from the Census of Retail Trade and are the level of
concentration in a given year with markets defined according to the noted
geography. All local measures of concentration use the establishments included
in the sample for the product-based results. Industry concentration uses six-
digit NAICS codes. (CBDRB-FY20-P1975-R8604, CBDRB-FY19-P1179-R7207)

Figure 5: Product vs Industry Concentration Notes: The data are from the
Census of Retail Trade. Each point marks the change in local Herfindahl-
Hirschman Index (HHI) of a product category and its main subsector between
1992 and 2012. Markets are defined at the commuting zone level and are
aggregated using each market’s share of national sales in the relevant
industry or product. (CBDRB-FY20-P1975-R8604)

We match each product to the subsector that primarily sells that product
(e.g., Clothing and NAICS 448: Clothing and Clothing Accessory Stores) and
plot the changes in concentration in Figure 5. The figure shows a positive
correlation between industry and product concentration despite the differences
in market definition. However, the increases in concentration are larger when
measured at the industry level, which explains the larger increases in overall
retail concentration shown in Table 3. Appendix D.6 complements these results
by reporting the levels of local and national concentration for the industries
corresponding to our main product categories and general merchandisers.

The picture that emerges from our data differs from Rossi-Hansberg et al.
((2021), who find a decrease in industrial retail concentration at the zip
code level of 17 percentage points between 1992 and 2012. Our studies differ
in both data and methodology.

Rossi-Hansberg et al. use U.S. National Establishment Time Series (NETS) data,
a private dataset, to calculate concentration using sales and employment for
multiple sectors.161616 Crane and Decker ((2020) show that the NETS has issues
tracking establishments over time, making it problematic for measuring trends
and Decker ((2020) argues that NETS sales are typically imputed from
employment, making studies with NETS most comparable to studies of employment
concentration.  The NETS defines the retail sector using Standard Industrial
Classification (SIC) codes, while the CRT uses NAICS. The main difference is
that SIC includes restaurants in retail while the NAICS does not, making it so
that our results are not directly comparable ((Trachter, 2021).

We also differ in the aggregation methodology for local concentration. The
methodology in Rossi-Hansberg et al. places more weight on markets with
declining concentration because it uses each market’s final share of
employment and markets become less concentrated as they grow. Weighting
markets using their average share of employment over time or their initial
share always implies increasing local concentration.

We replicate the methodology of Rossi-Hansberg et al. in our data and find a
1.5 percentage point decrease in local industrial concentration at the zip
code level. The remaining 15.5 percentage points between our results are
equally due to differences in market definition and data sources. For their
baseline result, Rossi-Hansberg et al. define markets based on eight-digit SIC
codes, while we use six-digit NAICS codes in our industry measures.171717
Eight-digit SIC codes may be overly detailed for retail markets because many
retailers will sell multiple types of goods. For example, concentration in
eggs and poultry (54999902) would miss the fact that many eggs and poultry are
sold by chain grocery stores (54119904) and discount department stores
(53119901).  Rossi-Hansberg et al. show that moving from eight- to four-digit
SIC codes in NETS implies a decline in concentration of 8 percent, explaining
about half of the difference between our results. Four-digit SIC codes are
comparable to the six-digit NAICS available in the CRT. The change from NETS
data to CRT data explains the other half of the difference. We provide full
details of these exercises in Appendix E.

All other concentration measures we calculate for the retail sector—varying
the level of geographical aggregation, aggregation methodology, and definition
of markets by product or industry—imply an increase in local concentration
between 1992 and 2012. Taken together, we find robust evidence for increases
in local retail concentration.

###  4 The Relationship Between National and Local HHIs

We now turn to the relationship between national and local concentration, and
the role of single- and multi-market firms in shaping this relationship.
National concentration can increase as single- and multi-market firms
consolidate in local markets and increase local concentration. But
concentration can also increase as multi-market firms expand across markets,
capturing a larger share of national sales without necessarily increasing
local concentration. This expansion makes it so that consumers in different
markets increasingly buy from the same firms. We refer to this as cross-market
concentration.

We disentangle the contribution of consolidation and expansion of single- and
multi-market retailers in increasing national concentration in three steps.
First, we show that the contribution of single-market firms is negligible.
Then, we establish that this is necessarily the case given the distribution of
economic activity in the U.S. retail sector. Finally, we conduct a
counterfactual exercise to separate the impact of consolidation and expansion
in the growth of national concentration. We find that expansion plays a
prominent role between 1992–2002 explaining about 89 percent of the increase
in national concentration, with consolidation increasing in importance in the
1997–2007 period.

####  4.1 The Contribution of Single-Market Firms to Concentration

Single-market firms can only affect national trends through local
concentration as they do not affect cross-market concentration. To quantify
their role, we consider a counterfactual where all firms are single-market
firms by breaking up multi-market firms into separate firms in each commuting
zone. This counterfactual gives us an upper bound on the role of single-market
firms in explaining national trends, while keeping the level and evolution of
local concentration unchanged.

If all firms operated as single-market firms, the national HHI would have been
0.06 percent in 1992 and 0.07 percent in 2012. These counterfactual levels are
95-98 percent smaller than the actual national HHI, showing that the increase
in local concentration coming from single-market firms cannot explain the
evolution of U.S. retail concentration.181818 Similar patterns arise for
individual product markets. The level of the product HHI in the counterfactual
varies between 0.03 and 0.14 percent and remain flat between 1992 and 2012.

This exercise further implies that, in the U.S., national retail trends must
be due to changes in cross-market concentration and therefore to the behavior
of multi-market firms. We make this precise by decomposing the national HHI
into the role of local and cross-market concentration. Recall that the HHI for
product $j$ measures the probability that two dollars, $x$ and $y$, chosen at
random, are spent at the same firm. Using the Law of Total Probability we
decompose the national HHI based on whether the two dollars are spent in the
same or different markets:191919 The same principle also applies in other
settings. We can use the law of total probability to decompose the HHI into
any set of mutually exclusive components. These can be the urban or rural
markets, or markets with different demographic characteristics. We provide a
detailed description of the decomposition in Appendix A.

$\displaystyle\underbrace{P(i_{x}=i_{y})}_{\textrm{National
HHI}}=\overbrace{P(\ell_{x}=\ell_{y})}^{\textrm{Collocation}}\underbrace{P(i_{x}=i_{y}|\ell_{x}=\ell_{y})}_{\textrm{Local
HHI}}+\overbrace{P(\ell_{x}\neq\ell_{y})}^{\textrm{1 --
Collocation}}\underbrace{P(i_{x}=i_{y}|\ell_{x}\neq\ell_{y})}_{\textrm{Cross-
Market Concentration}},$ (5)

where $i_{x}$ is the firm at which dollar $x$ is spent and $\ell_{x}$ is the
location of the market in which dollar $x$ is spent, and likewise for $y$.

Equation (5) has three components. The first component,
$P(\ell_{x}=\ell_{y})$, which we term collocation, captures the probability
that two dollars are spent in the same location. The second component,
$P(i_{x}=i_{y}|\ell_{x}=\ell_{y})$, is an aggregate index of local
concentration, with local concentration measured as in equation (2). This
captures the extent to which consumers in a local market shop at the same
firm. The third component, $P(i_{x}=i_{y}|\ell_{x}\neq\ell_{y})$, captures
cross-market concentration, the probability that a dollar spent in different
markets is spent at the same firm.

The decomposition shows that 98 percent of the level of national concentration
comes from the cross-market term. The reason for this is that, in the U.S.,
even the largest markets represent only a small fraction of total retail
sales, resulting in a low collocation term. This limits the impact that
concentration on local markets on its own can have on national trends.202020
The collocation term is
$P(\ell_{x}=\ell_{y})=\sum_{\ell=1}^{L}\left(s_{\ell}\right)^{2},$ where
$s_{\ell}$ is the share of location $\ell$ in national sales. Our estimates of
the collocation term for the retail sector using confidential data are about
0.012. See figures A.1 and A.2 in Appendix A.  For national and local
concentration to increase as we observe, it must be that the increase in local
concentration is accompanied by cross-market concentration, with consumers in
different locations increasingly shopping at the same (large) firms. This can
only happen via the consolidation and expansion of multi-market firms.

####  4.2 The Contribution of Multi-Market Firms to Concentration

The previous results show that the increase in national retail concentration
reflects the activity of multi-market firms, particularly that of the largest
retailers, that affect cross-market concentration through their expansion and
consolidation across markets. Take, for instance, the behavior of firms
present in at least 50 commuting zones. Table 4 shows that their share of
national sales increased from 34 percent to 58 percent between 1992 and 2012,
despite there being no more than 350 of these firms in the U.S.. By contrast,
their average local share increased only slightly from 3.2 to 3.4 percent.
This suggests that the increase in U.S. retail concentration is mostly due to
the expansion of multi-market retailers into new markets, rather than
consolidation in the markets they were already present in.212121 In fact,
large retailers went from being present in 139 commuting zones on average in
1992 to 163 commuting zones in 2012, an increase of 27 percent. This adds to
the findings of Cao et al. ((2019), Hsieh and Rossi-Hansberg ((2023), and
Rossi-Hansberg et al. ((2021), who also highlight the role of firm expansion.

Table 4: Multi-Market Firms Present in at Least 50 Commuting Zones

| 1992 | 2002 | 2012
---|---|---|---
Commuting Zones per firm | 131.5 | 154.7 | 169.2
Establishments per firm | 616.2 | 686.7 | 814.9
National market share | 0.388 | 0.533 | 0.581
Local market share | 0.032 | 0.033 | 0.034

  * •

Notes: The numbers come from the Census of Retail Trade and report averages
across retailers with establishments in at least 50 commuting zones in a given
year. National market share is the total sales of establishments of these
firms in sales of product categories in our sample divided by total sales of
product categories in sample. The local market share is a simple average
across commuting zones, product categories, and firms of the market share of
firms active in a given product category and commuting zone in a given year.
(CBDRB-FY23-P1975-R10585)

We find that most of the increase in U.S. retail concentration comes from the
expansion of multi-market retailers, with consolidation in markets they are
already in playing a minor role. We do this by taking into account the
behavior of all U.S. retailers and conducting an additional counterfactual
exercise that allows us to isolate the changes in national concentration
coming from higher concentration at the local level (consolidation) from those
coming from the expansion of firms across markets, all while being consistent
with the observed evolution of local concentration.

To isolate the contribution of within-market consolidation, we generate a
counterfactual economy where the rank of firms is preserved across time.222222
We thank an anonymous referee for suggesting this exercise.  This means that
the identity of the leader in each market is counterfactually preserved, as is
the identity of the rth largest firm in the market at time $t$, and they are
assigned the sales share of the corresponding rth largest firm in the market
at time $t^{\prime}$. In this way, the counterfactual economy assigns the
increases in local market shares to consolidation of existing firms (the
previous leaders) and not to changes induced by the expansion of firms into
new markets. The counterfactual preserves the local market structure of time
$t$ and replicates the changes in local concentration by construction.

Formally, for each product $j$, we consider all firms $f$ active at some time
$t$ in each location $\ell$ and record their rank
$r(f,j,\ell,t)\in\left\\{1,\ldots,N_{j\ell}^{t}\right\\}$. These ranks capture
the market structure at time $t$ in each local product market. We then
consider a future time $t^{\prime}$ and assign to each firm $f$ active at time
$t$ the share of the firm with the same rank $r(f,j,\ell,t)$ operating in time
$t^{\prime}$: $\tilde{s}_{f}^{j\ell
t^{\prime}}=s_{i(r(f,j,\ell,t),j,\ell,t)}^{j\ell t^{\prime}}$, where
$i(r,j,\ell,t^{\prime})$ gives the identity of the $r^{th}$ largest firm
selling product $j$, in location $\ell$ at time $t^{\prime}$ and
$s_{i(r(f,j,\ell,t),j,\ell,t)}^{j\ell t^{\prime}}=0$ if
$r(f,j,\ell,t)>N_{j\ell}^{t^{\prime}}$. So that the counterfactual matches the
evolution of local concentration, we first assign market shares to the
$N_{j\ell}^{t}$ firms operating at time $t$ and then assign any remaining
market shares to entrants (in order of rank in $t^{\prime}$). Having completed
this process, we aggregate the counterfactual shares at the national level,
$\tilde{s}_{f}^{jt^{\prime}}=\sum_{\ell}\tilde{s}_{f}^{j\ell t^{\prime}}$ and
compute the national HHI as in (1).

Figure 6: National Concentration Without Retailers’ Expansion Notes: The
numbers are based on calculations from the Census of Retail Trade. The figure
reports the level of the national HHI as defined in equation 1 and its
counterfactual levels preserving the market structure of each Census year. The
counterfactual values are computed by preserving the rank of firms according
to the initial market structure, assigning to the firm with the $r^{th}$
largest shares in the initial year the market share of the $r^{th}$ firm in
each subsequent year. The numbers for this figure are presented in Table D.4
of Appendix D.7. (CBDRB-FY23-P1975-R10585)

We conduct the counterfactual taking the market structure of each census year
and present the results in Figure 6. Without the expansion of retailers across
markets the national HHI would have only increased 0.33 percentage points
between 1992 and 2012, this is just 11 percent of the observed change in
concentration. The share of the increase in concentration accounted for
within-market consolidation does rise when we start from the 1997 or 2002
market structure. Consolidation explains up to 40 percent of the increase in
the 1997–2007 period, the years when national concentration increased the
most. Nevertheless, the message is clear. The majority of the increase in U.S.
retail concentration comes from the increase in the market share of multi-
market retailers as they expand into new markets.

The same pattern of low but increasing importance of consolidation holds when
we look at the evolution of concentration across product categories. Take, for
example, the largest product category, groceries. Where expansion accounts for
92 percent of the change in national concentration between 1992 and 2002,
falling to 80 percent between 2002 and 2012. These results align with the
behavior of large general merchandisers like Walmart, that expanded into new
markets during the 1980s and 1990s ((Holmes, 2011, Fig. 2, pg. 255) and went
from not selling groceries to being the largest grocer in the U.S. ((Basker,
2007). We extend these results and show that within-market consolidation plays
a larger role in the period after 1997. Our data indicates that this was part
of a broader phenomena across multiple product categories. However, there are
two categories that stand as outliers. Consolidation captures less than 2
percent of the increase in concentration in Clothing between 1992 and 2002,
while it accounts for 60 percent of the increase in concentration in Sporting
Goods between 1992 and 2002, and 84 percent between 2002 and 2012.

###  5 Local Retail Concentration and Retailers’ Margins

The previous sections document increases in product- and industry-based
measures of local retail concentration that are broad based and follow the
overall trend of higher national concentration in Retail and other sectors.
These trends in concentration can imply higher markups and ultimately affect
consumer prices. However, studying this relationship is challenging because
long series on prices or costs for U.S. retailers are unavailable. We now
provide a discussion of the magnitude of these effects in light of the
observed increases in retailers’ gross margins.

To get a sense of the potential effect of concentration on markups and deal
with data limitations, we use the relationship between market profitability
and market concentration as measured by the HHI that arises under Cournot
competition ((e.g., Tirole, 1988, pg. 221-223). The gross margins $(\mu)$ in a
local product or industry market satisfy232323 The relationship above applies
when goods are homogeneous, however, we generalize it to the case in which
goods are differentiated and preferences are homothetic in Appendix F. Then,
the gross-margin is approximately given by
$\mu=\frac{\varepsilon}{\varepsilon-1}\left[1-\text{HHI}\right]^{-1}$. This is
the same relationship between gross margins and concentration in models of
oligopolistic competition like Atkeson and Burstein ((2008) and Grassi
((2017).

$\displaystyle\mu\equiv\frac{\text{Revenue}}{\text{Cost of Goods
Sold}}=\left[1-\frac{\text{HHI}}{\varepsilon}\right]^{-1},$ (6)

where $\varepsilon$ is the elasticity of demand. This relationship gives us a
measure of the effect of the change in local concentration on retailers’
margins coming from the increased market power of retailers in the local
markets they operate in.

Table 5: Change in Retailers’ Margins: 1992-2012

| Products $(\Delta\mu)$ | Industry $(\Delta\mu)$
---|---|---
| $\varepsilon=1.5$ | $\varepsilon=3$ | $\varepsilon=6$ | $\varepsilon=1.5$ | $\varepsilon=3$ | $\varepsilon=6$
Commuting Zone | 1.59 | 0.75 | 0.37 | 11.89 | 4.95 | 2.27
Zip Code | 1.27 | 0.52 | 0.23 | 14.87 | 4.34 | 1.74

  * •

Notes: The numbers are change in gross margins for the retail sector implied
by equation (6) for changes in product and industry HHIs for different
geographical definitions of local markets. The changes of the HHI are
calculated using Table 3. (CBDRB-FY20-P1975-R8604)

We use our measures of the local HHI for product and industry markets to get
the changes in firms’ margins between 1992 and 2012 implied by equation (6).
We do this for different values of the elasticity of demand based on the range
of estimates in Brand ((2020, fig. 3). As shown in Table 5, the change in
local product concentration implies an increase in margins of 1.6 percentage
points for a low value of $\varepsilon$, but the number is cut almost by half
for larger values of the elasticity of demand. The changes implied by industry
concentration are much larger, reflecting the findings of Section 3.4
documenting that the increases in concentration are larger at the industry
than at the product level. Industry concentration implies increases in markups
between 14.9 and 1.7 percentage points. However, these magnitudes can be
misleading as they do not take into account cross-industry competition taking
place in retail.

The change in margins in product markets implied by local product
concentration is meaningful and accounts for about one-fourth of the observed
changes in retailers gross margins from the Annual Retail Trade Survey
(ARTS).242424 The changes in markups implied by local concentration as well as
the changes in retailers gross margins from the ARTS are significantly lower
than those found for retail by De Loecker et al. ((2020, fig. VI).  The ARTS
data show an increase in retailers’ margins of 6.0 percentage points between
1993 and 2012 ((U.S. Census Bureau, 1993-2012). Moreover, taking into account
the differences in concentration trends and elasticities of demand across
products implies a larger increase in margins. In Appendix G, we estimate a
model of oligopolistic competition in local product markets based on Atkeson
and Burstein ((2008) and find that average product markups increase by 2.1
percentage points between 1992 and 2012, or about one-third of the increase in
margins reported in the ARTS.

Looking forward, the growth of multi-market and online retail presents new
challenges for understanding retail markets. There is evidence that multi-
market firms charge uniform prices across locations ((Adams and Williams,
2019; Dellavigna and Gentzkow, 2019). This practice initially leads to lower
markups because larger (less concentrated) markets have more weight in the
pricing decisions of multi-market retailers (Appendix G.6). Simultaneously,
the growth of e-commerce has led to new options for consumers in all markets,
but much of this growth is due to a few large firms and may have caused the
closing of brick-and-mortar retailers.

###  6 Conclusion

Consumers have traditionally chosen between nearby stores selling a given
product when purchasing goods. This fact makes local market conditions
relevant for assessing the competitive environment in the retail sector.
Accordingly, we measure concentration on local product markets using novel
Census data on all U.S. retailers. We find increases in concentration covering
the majority of markets which hold for product- and industry-based measures of
concentration, even after taking into account the role of online and other
non-store retailers. These trends match that of national retail concentration
that also rises strongly between 1992 and 2012.

Further, we show that the trends of increasing national and local
concentration are linked through the expansion and consolidation of multi-
market firms, with single-market firms playing no role in the increase of
national concentration. We find that the observed increases in national
concentration between 1992 and 2002 are due mostly to the expansion of multi-
market firms into new markets, with consolidation of these firms in the
markets they operate in increasing in importance in the 2002-2007 period.

The increases in local concentration that we document can account for one-
quarter to one-third of the rise in retailers’ gross margins observed in the
retail sector by increasing retailers’ local market power. This can reflect an
increase in markups that can potentially hurt consumers. However, if increases
in concentration are caused by low-cost multi-market firms increasing their
market share, prices may fall despite increases in markups ((Bresnahan, 1989).
In fact, the 1.6 percentage point increase in markups due to local
concentration is small relative to the 34 percent decrease in relative retail
prices observed in the same period. These cost advantages may be due to direct
foreign sourcing ((Smith, 2019), negotiating power with suppliers ((Benkard et
al., 2021), or investments in information and communication technologies
((Hsieh and Rossi-Hansberg, 2023). Moreover, increases in e-commerce
penetration since 2012 may have tempered the increasing trends in local
concentration.

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## Online Appendix

The Evolution of U.S. Retail Concentration111Any views expressed are those of
the authors and not those of the U.S. Census Bureau. The Census Bureau’s
Disclosure Review Board and Disclosure Avoidance Officers have reviewed this
information product for unauthorized disclosure of confidential information
and have approved the disclosure avoidance practices applied to this release.
This research was performed at a Federal Statistical Research Data Center
under FSRDC Project Numbers 1179 and 1975 (CBDRB-FY19-P1179-R7207, CBDRB-
FY20-P1975-R8604 and CBDRB-FY23-P1975-R10585).

Dominic A. Smith222Bureau of Labor Statistics; Email<EMAIL_ADDRESS>Web: https://www.bls.gov/pir/authors/smith.htm. & Sergio Ocampo333University
of Western Ontario; Email<EMAIL_ADDRESS>Web:
https://sites.google.com/site/sergiocampod/.

###  Appendix A Concentration Decomposition

We calculate the HHI for the retail sector at a time $t$, as the sales-
weighted average of the product-HHIs:

$\displaystyle HHI^{t}\equiv\sum_{j=1}^{J}s_{j}^{t}HHI_{j}^{t}.$ (A.1)

The HHI for a given product $j$, $HHI_{j}^{t}$, can be decomposed into the
contribution of local and cross-market concentration. The decomposition starts
from the probability that two dollars $(x,y)$ spent on a product during some
time period are spent at the same firm $(i)$, which gives the HHI at the
national level:

$\displaystyle HHI_{j}^{t}\equiv
P(i_{x}=i_{y};j,t)=\sum_{i}\left(s_{i}^{jt}\right)^{2},$ (A.2)

where $s_{i}^{jt}$ is the share of firm $i$ in product $j$ during period $t$.
This probability can be divided into two terms by conditioning on the dollars
being spent in the same location, $\ell_{x}=\ell_{y}$:

$\displaystyle P(i_{x}=i_{y};j,t)$
$\displaystyle=\underbrace{\overbrace{P(i_{x}=i_{y}|\ell_{x}=\ell_{y};j,t)}^{\text{Local
Concentration}}\overbrace{P(\ell_{x}=\ell_{y};j,t)}^{\text{Collocation}}}_{\textbf{Local
Term}}$ (A.3)
$\displaystyle\qquad+\underbrace{\overbrace{P(i_{x}=i_{y}|\ell_{x}\neq\ell_{y};j,t)}^{\text{Cross-
Market Concentration}}\overbrace{P(\ell_{x}\neq\ell_{y};j,t)}^{\text{1 -
Collocation}}}_{\textbf{Cross-Market Term}}.$

When we report contribution of local and cross-market concentration for the
retail sector, we report the sales-weighted average of these two terms across
products.

The collocation probability is calculated as:

$\displaystyle P(\ell_{x}=\ell_{y};j,t)$
$\displaystyle=\sum_{\ell=1}^{L}\left(s_{\ell}^{jt}\right)^{2}.$ (A.4)

When we report the collocation for the retail sector, we report the sales-
weighted average of collocation across products:
$\text{Collocation}_{t}=\sum_{j}s_{j}^{t}P(\ell_{x}=\ell_{y};j,t)$.

The first component, $P(i_{x}=i_{y}|\ell_{x}=\ell_{y})$, is an aggregate index
of local concentration, with local concentration measured as in equation
(2).444 In the decomposition, each local market is weighted by the conditional
probability that the two dollars are spent in location $\ell$ given that they
are spent in the same location:
$\nicefrac{{s_{\ell}^{2}}}{{\left(1-\sum_{p}s_{p}^{2}\right)}}$. These weights
give more importance to larger markets than the more usual weights
$s_{\ell}$—the share of sales (of product $j$) accounted for by location
$\ell$ (at time $t$). We present aggregated series for local concentration in
Section 3 that use the latter weights. Appendix A derives these results in
detail.  This captures the extent to which consumers in a local market shop at
the same firm. Local concentration is calculated as:

$\displaystyle P\left(i_{x}=i_{y}|\ell_{x}=\ell_{y};j,t\right)$
$\displaystyle=\sum_{\ell=1}^{L}\underbrace{P\left(\ell_{x}=\ell|\ell_{x}=\ell_{y};j,t\right)}_{\text{Location
Weights}}\overbrace{P\left(i_{x}=i_{y}|\ell_{x}=\ell,\ell_{x}=\ell_{y};j,t\right)}^{\text{Local
HHI}}$
$\displaystyle=\sum_{\ell=1}^{L}\frac{(s_{\ell}^{jt})^{2}}{\sum_{n}(s_{n}^{jt})^{2}}\sum_{k=1}^{K}\left(s_{k}^{j\ell
t}\right)^{2}.$ (A.5)

In the main text, when we report the local HHI for individual product
categories we also report the retail sector’s average local HHI using sales
weights instead of the weights implied by the decomposition to facilitate
comparison to other research:

$\displaystyle\text{HHI}_{t}^{\text{Local}}=\sum_{j}^{J}s_{j}^{t}\sum_{\ell}^{L}s_{\ell}^{jt}\sum_{i}\left(s_{i}^{j\ell
t}\right)^{2}.$ (A.6)

The third component, $P(i_{x}=i_{y}|\ell_{x}\neq\ell_{y})$, which we call
cross-market concentration, captures the probability that a dollar spent in
different markets is spent at the same firm:

$\displaystyle
P(i_{x}=i_{y}|\ell_{x}\neq\ell_{y})=\underbrace{\sum_{\ell}\sum_{n\neq\ell}\frac{s_{\ell}s_{n}}{1-\sum_{p}s_{p}^{2}}}_{\textrm{Weights}}\underbrace{\sum_{i=1}^{N}s_{i}^{\ell}s_{i}^{n}}_{\textrm{Cross-
Market}}.$ (A.7)

The cross-market concentration between two markets (say $\ell$ and $n$) is
given by the product of the shares of the firms in each location (the
probability that two dollars spent in different locations are spent in the
same firm). The pairs of markets are then weighted by their share of sales and
are summed.

The cross-market term as a whole is calculated as:

$\displaystyle
P\left(\ell_{x}=\ell_{y};j,t\right)P\left(i_{x}=i_{y}|\ell_{x}\neq\ell_{y};j,t\right)$
$\displaystyle=(1-\sum_{\ell=1}^{L}\left(s_{\ell}^{jt}\right)^{2})\sum_{k=1}^{L}\sum_{\ell\neq
k}\frac{s_{k}^{jt}s_{\ell}^{jt}}{1-\sum_{m}^{L}\left(s_{m}^{jt}\right)^{2}}\sum_{i=1}^{I}s_{i}^{kjt}s_{i}^{\ell
jt}$ $\displaystyle=\sum_{k=1}^{L}\sum_{\ell\neq
k}s_{k}^{jt}s_{\ell}^{jt}\sum_{i=1}^{I}s_{i}^{kjt}s_{i}^{j\ell t}.$

This calculation is the same in the results for product category because
$1-\sum_{m}^{L}\left(s_{m}^{jt}\right)^{2}$ cancels in the calculation of the
collocation term.

As mentioned in the main text, the collocation term determines how much purely
local concentration (without cross-market linkages) can affect national
concentration terms. Conversely, the collocation term determines how much can
be learned about local competitive environments using national information. If
it were large enough, national concentration numbers can be informative about
local markets. However, the collocation term for the U.S. retail sector is low
and remarkably stable across time and products. This implies that local
concentration can only have a limited effect on national trends, making
changes in national concentration mostly informative about cross-market
concentration.

Figure A.1: Share of Local Concentration Term in National Concentration Notes:
The numbers are based on calculations from the Census of Retail Trade. The
share of local concentration is measured as the ratio of the local
concentration term in equation (5) to the national Herfindahl-Hirschman Index
(HHI). The local concentration term is the product of the collocation term and
local HHI. (CBDRB-FY20-P1975-R8604)

Figure A.1 shows the contribution of local concentration to the level national
concentration by year, defined as the ratio of the local term in the
decomposition to the national HHI,
$\nicefrac{{P(\ell_{x}=\ell_{y})P(i_{x}=i_{y}|\ell_{x}=\ell_{y})}}{{P(i_{x}=i_{y})}}$.
The contribution of local concentration to national concentration is
small—never above 5 percent. Moreover, the contribution of local concentration
to national concentration has been falling over time as national concentration
has been increasing. By 2012, local concentration accounted for just 1.7
percent of the national concentration level.

The pattern of low collocation terms and a prominent role of cross-market
concentration applies across all product categories. Figure A.2 shows that the
collocation term is always low, less than 2 percent, and stable over time. By
the early 1990s, only furniture and groceries have contributions of over 10
percent, with the local contribution in all other products being no higher
than 5.5 percent, and as low as 2 percent.

Figure A.2: Collocation across Product Categories Notes: The numbers are
collocation indexes by product weighted by market size from the Census of
Retail Trade. (CBDRB-FY20-P1975-R8604)

###  Appendix B Cleaning and Aggregating Product Lines Data

The Economic Census collects data on establishment-level sales in a number of
product categories (Figure B.1 provides an example form). Many establishments
have missing product line sales either due to them not responding to questions
or because they do not receive a form.555Establishments of large firms are
always mailed a form, but small firms are sampled. In total, reported product
lines data account for about 80 percent of sales. We develop an algorithm to
impute data for missing establishments, which involves aggregating product
line codes into categories such that we can accurately infer each
establishment’s sales by category with available information. For example, we
aggregate lines for women’s clothes, men’s clothes, children’s clothes, and
footwear into a product category called clothing.

We then establish 18 product categories detailed in Table B.1. Of these 18
product categories, 8 categories that we label “Main” account for over 80
percent of store sales in the sample. The other 10 product categories are
specialty categories that account for a small fraction of aggregate sales and
are sold primarily by establishments in one specific industry. For example,
glasses are sold almost exclusively by establishments in 446130 (optical goods
stores). We create these categories so that establishments that sell these
products are not included in concentration measures for the 8 main product
categories.

Figure B.1: Sample Product Lines Form

####  B.1 Aggregating Product Lines

The first step of cleaning the data is to aggregate reported broad and
detailed product line codes into categories. Some codes reported by retailers
do not correspond to valid product line codes, and we allocate those sales to
a miscellaneous category. The Census analyzes reported product line codes to
check for issues and flags observations as usable if they pass this check. We
include only observations that are usable and then map these codes to
categories. We use the reported percentage of total sales accounted for by
each product line instead of the dollar value because the dollar value is
often missing. Typically an establishment either reports product line data for
100 percent of its sales or does not report any data. For the small number of
establishments that report product lines data summing to a number other than
100 percent, we rescale the percentages so that they sum to one.666This
procedure has a minimal effect on aggregate retail sales in each category.
After this procedure, we have sales by product category for all establishments
that reported lines data. The resulting categories are listed in Table B.1.

Table B.1: List of Product Categories

Product Category | Main | Corresponding Industry | Example Firm
---|---|---|---
Automotive Goods | N | 441 | Ford Dealer
Clothing | Y | 448 | Old Navy
Electronics and Appliances | Y | 443 | Best Buy
Furniture | Y | 442 | Ikea
Services | N | N/A |
Other Retail Goods | N | N/A |
Groceries | Y | 445 | Trader Joe’s
Health Products | Y | 446 | CVS
Fuel | N | 447 | Shell Gasoline
Sporting Goods | Y | 451 | Dick’s Sporting Goods
Toys | Y | 451 | Toys “R” Us
Home & Garden | Y | 444 | Home Depot
Paper Products | N | 453210 |
Jewelry | N | 423940 | Jared
Luggage | N | 448320 | Samsonite
Optical Goods | N | 446130 | Lenscrafters
Non-Retail Goods | N | N/A |
Books | N | 451211 | Borders

  * •

Notes: Authors’ created list of product categories. The Main column indicates
that a product category is included in concentration calculations. Firm names
were created for illustrative purposes based on industries reported to the
Securities and Exchange Commission and do not imply that the firm is in the
analytical sample.

####  B.2 Imputing Missing Data

For the remaining establishments, we impute data using the NAICS code of the
establishment, reported sales of other establishments of the same firm in the
same industry, and reported activity of the same establishment in other census
years.777Reported product line sales are very similar across establishments of
the same firm and the same establishment over time. Most establishments are
part of single-unit firms, and many do not appear in multiple census years;
thus their sales are imputed using only industry information.

Using this aggregation method, almost all establishments have significant
sales in only two product categories, which increases confidence in the
imputation. Additionally, we have compared the aggregate sales in our data to
the Consumer Expenditure Survey (an independent Bureau of Labor Statistics
program), and they are in line with the numbers from that source.888Retail
sales include some sales to companies, so it is expected that retail sales in
a product category exceed consumer spending on that category.

Where relevant, all sales are deflated using consumer price indexes ((U.S.
Bureau of Labor Statistics, 1982-2012). We use the food deflator for
Groceries, clothing and apparel deflator for Clothing, and the deflator for
all goods excluding food and fuel for all other categories.

We find that this procedure predicts sales accurately for most establishments,
but a small number of stores in each industry report selling very different
products than all other stores in that industry. In these cases, the
prediction can produce substantial error.

###  Appendix C Product vs Industry in the CRT

In this section, we provide more information about the retail industries in
our sample and how they compare to the products that we study. At the highest
level of detail there are 61 NAICS industries that are comparable to our
products. However, eight of the 61 industries account for two-thirds of sales,
implying that retail sales are concentrated in small number of NAICS codes.
Moreover, many of the largest industries sell the same sets of products such
as clothing and groceries.

####  C.1 Number of six-digit NAICS Industries

Since the introduction of NAICS in 1997, there have consistently been about 70
NAICS codes with minor changes in each NAICS revision. We exclude the 10 codes
related to automotive industries and fuel dealers (see Section 2). That leaves
about 60 industries which primarily sell goods covered by the product
categories we use. In 2002, specifically, there were 61 six-digit NAICS codes
belonging to 22 four-digit industry groups. Retail industry groups and
subsectors (three-digit NAICS) have not been changed since NAICS was
introduced.

Table C.1: NAICS codes by level of Detail

Name | Number of digits | Number of codes
---|---|---
Subsector | 3 | 5
Industry Group | 4 | 22
Industry | 6 | 61

  * •

Notes: The table indicates the number of NAICS codes in the retail sector
(NAICS 44-45) using 2002 NAICS codes. Name is the official title of the
grouping with a given number of digits. Number of codes is the number of
unique codes of a given length included in this papers’ sample. Codes in
subsectors 441 and 447 are not included in any results in this paper except
table E.1.

####  C.2 Concentration in Products and Industries

Although there are many industries in retail, a small number of them account
for the majority of sales as is shown in Table C.2. In 2002, the largest five
industries accounted for 54 percent of sales within the 61 industries that we
focus on. The largest eight industries accounted for 65 percent of sales which
is lower than the 94 percent of sales accounted for by the eight main product
categories in our study, but still large. The largest 18 industries account
for 81 percent of sales leaving only 19 percent of sales for the remaining 43
industries. In fact, Table C.3 shows that only 24 industries have a sales-
share of more than one percent of retail sales and only 32 industries have a
sales share of more than half of one percent. The remaining 29 retail
industries are individually small and together account for only 5.5 percent of
retail sales.

Table C.2: Share of Sales by Largest Industries

Number of Codes | Industry Share | Product Share
---|---|---
5 | 54 | N/A
8 | 65 | 94
10 | 70 | N/A
18 | 81 | 100
25 | 89 | N/A

  * •

Notes: The table shows the sales share in retail for different groups of
6-digit NAICS industries or product categories.

Table C.3: Share of Sales by NAICS Industry

Rank | Industry | Name | Share | Cumulative
---|---|---|---|---
1 | 445110 | Supermarkets and other grocery stores | $22.0$ | $22.0$
2 | 452910 | Warehouse clubs and supercenters | $10.6$ | $32.5$
3 | 446110 | Pharmacies and drug stores | $8.7$ | $41.2$
4 | 452112 | Discount department stores | $7.5$ | $48.7$
5 | 454113 | Mail-order houses | $5.3$ | $54.0$
6 | 452111 | Department stores (except discount dept stores) | $5.0$ | $59.0$
7 | 448140 | Family clothing stores | $3.5$ | $62.5$
8 | 442110 | Furniture stores | $2.8$ | $65.2$
9 | 443112 | Radio, television, and other electronics stores | $2.7$ | $68.0$
10 | 448120 | Women’s clothing stores | $1.7$ | $69.7$
11 | 452990 | All other general merchandise stores | $1.7$ | $71.4$
12 | 445310 | Beer, wine, and liquor stores | $1.5$ | $73.0$
13 | 444220 | Nursery, garden center, and farm supply stores | $1.5$ | $74.5$
14 | 454111 | Electronic shopping | $1.5$ | $75.9$
15 | 451110 | Sporting goods stores | $1.4$ | $77.3$
16 | 448310 | Jewelry stores | $1.3$ | $78.6$
17 | 448210 | Shoe stores | $1.3$ | $79.9$
18 | 454390 | Other direct selling establishments | $1.2$ | $81.1$
19 | 442299 | All other home furnishings stores | $1.2$ | $82.4$
20 | 445120 | Convenience stores | $1.2$ | $83.5$
21 | 453210 | Office supplies and stationery stores | $1.1$ | $84.7$
22 | 451120 | Hobby, toy, game stores | $1.0$ | $85.7$
23 | 442210 | Floor covering stores | $1.0$ | $86.7$
24 | 443120 | Computer and software stores | $1.0$ | $87.7$
25 | 453220 | Gift, novelty, souvenir stores | $0.9$ | $88.5$
26 | 454311 | Heating oil dealers | $0.8$ | $89.4$
27 | 451211 | Book stores | $0.8$ | $90.2$
28 | 443111 | Household appliance stores | $0.8$ | $91.0$
29 | 453998 | Other miscellaneous store retailers | $0.6$ | $91.6$
30 | 453930 | Manufactured (mobile) home dealers | $0.5$ | $92.1$
31 | 454312 | Liquefied petroleum gas (bottled gas) dealers | $0.5$ | $92.7$
32 | 448190 | Other clothing stores | $0.5$ | $93.2$
33 | 448110 | Men’s clothing stores | $0.4$ | $93.6$
34 | 453310 | Used merchandise stores | $0.4$ | $94.0$
35 | 453910 | Pet and pet supplies stores | $0.4$ | $94.5$

  * •

Notes: The table shows the share of sales in retail (excluding 441 and 447)
that are accounted for by each industry. Cumulative shows the fraction of
sales accounted for by the X largest industries. Some industry names have been
edited for space. Authors’ calculations using the 2002 Economic Census Table
ec0244i1 ((U.S. Census Bureau, 2002). The share and cummulative columns may
not sum due to rounding.

####  C.3 Industries sell many products: Clothing Example

Having argued that industries and product categories have similar levels of
concentration we now show the overlap between industry sales and product
sales. We focus on the four product lines the comprise the Clothing product
category. In Table C.4, we show which industries account for sales in each of
the four product lines. We include all industries that are one of the top five
sellers of any of the four product lines. In the first three categories; men’s
clothes, women’s clothes, and children’s clothes no industry accounts for more
than 30 percent of sales of each line. These products are sold by stores in
four different subsectors (three-digit NAICS codes) showing that aggregating
industries would still miss the competition between retailers in the sales of
these product lines.

Table C.4: Share of Product Sales Accounted for by Each Industry - Clothing

|  | Men’s | Women’s | Children’s |
---|---|---|---|---|---
Industry Name | Clothing | Clothing | Clothing | Footwear
448110 | Men’s Clothing Stores | $12.0$ | $0.1$ | $0.3$ | $0.9$
448120 | Women’s Clothing Stores | $1.6$ | $22.1$ | $0.5$ | $2.3$
448130 | Children’s Clothing Stores | $0.1$ | $0.1$ | $18.4$ | $0.4$
448140 | Family Clothing Stores | $29.2$ | $23.3$ | $19.5$ | $8.6$
448210 | Footwear Stores | $2.0$ | $0.5$ | $0.6$ | $50.0$
451110 | Sporting Goods Stores | $4.1$ | $1.0$ | $0.9$ | $6.6$
452111 | Department Stores | $21.2$ | $21.5$ | $16.2$ | $14.1$
452112 | Discount Department Stores | $11.8$ | $10.9$ | $23.4$ | $6.1$
452910 | Warehouse Clubs & Supercenters | $7.3$ | $4.7$ | $11.4$ | $3.6$
454113 | Mail-order houses | $3.3$ | $5.6$ | $1.9$ | $3.6$
All Other Industries | $7.4$ | $10.2$ | $6.9$ | $3.8$
|  |  |  |  |

  * •

Notes: Numbers represent 100 multiplied by the share of sales in a product
line accounted for in each industry from Economic Census Table ec0244slls2
((U.S. Census Bureau, 2002) Numbers come from variable kbpct for the entire
U.S.. These numbers are based on public tables and do not include imputed
sales as described in Appendix B.

Table C.5 shows how sales within an industry are distributed across product
lines. There is one industry that specializes in each product. For example,
90.3 percent of the sales of 448110 (Men’s Clothing Stores) come from men’s
clothing. However, there are many industries that sell multiple product lines.
For example, 448140 (Family Clothing Stores) receives a significant amount of
revenue from each of the four lines. This fact motivates our decision to
combine the four lines into a clothing product category because it makes our
imputation procedure more reliable. Finally, there are the industries in the
general merchandising subsectors that each receive a significant amount of
revenue from outside of these four product lines. Similar patterns arise in
the other product categories.

Table C.5: Share of Industry Sales Accounted for by Each Product - Clothing

| Men’s | Women’s | Children’s |  |
---|---|---|---|---|---
| Clothing | Clothing | Clothing | Footwear | Other
448110 | $90.3$ | $2.2$ | $1.3$ | $4.4$ | $1.8$
448120 | $3.0$ | $87.9$ | $0.6$ | $3.1$ | $5.4$
448130 | $0.7$ | $1.0$ | $93.7$ | $2.5$ | $2.1$
448140 | $27.1$ | $44.5$ | $11.0$ | $5.5$ | $11.9$
448210 | $5.1$ | $2.5$ | $0.9$ | $89.8$ | $1.7$
451110 | $9.6$ | $4.8$ | $1.2$ | $10.8$ | $73.6$
452111 | $14.5$ | $30.2$ | $6.7$ | $6.7$ | $41.9$
452112 | $5.2$ | $9.9$ | $6.3$ | $1.9$ | $76.7$
452910 | $2.3$ | $3.0$ | $2.2$ | $0.8$ | $91.7$
454113 | $2.1$ | $7.1$ | $0.7$ | $1.5$ | $88.6$
|  |  |  |  |

  * •

Notes: Numbers represent 100 multiplied by the share of sales in a product
line accounted for in each industry from Economic Census Table ec0244slls1
((U.S. Census Bureau, 2002). Numbers come from variable lnpctal for the entire
U.S.. These numbers are based on public tables and do not include imputed
sales as described in Appendix B.

###  Appendix D Additional Tables and Figures

####  D.1 The Role of Multi-Product Retailers

Table D.1 shows how sales for each main product category are distributed
across sets of industries. This informs us of which type of establishment
accounts for the sales of each product. The main subsector column refers to
the NAICS subsector that most closely corresponds to the product category. The
NAICS code of the subsector is indicated next to each product category. The
main subsector accounts for just over half of sales on average, but this
figure varies depending on the product. A larger fraction of sales of
Furniture, Home Goods, and Groceries comes from establishments in their
respective NAICS subsectors, while Electronics and Toys are more commonly sold
by establishments in other subsectors. Over time, the share of sales accounted
by the product’s own subsector has decreased for most products, with the
difference captured by establishments outside of the general merchandise
subsector.

Table D.1: Share of Product Category Sales by Establishment Subsector

| Main Subsector | GM | Other
---|---|---|---
| 1992 | 2002 | 2012 | 1992 | 2002 | 2012 | 1992 | 2002 | 2012
Furniture (442) | 76.3 | 73.1 | 64.4 | 16.9 | 13.3 | 11.2 | 6.8 | 13.6 | 24.4
Clothing (448) | 50.9 | 51.8 | 51.1 | 41.4 | 37.7 | 27.4 | 7.7 | 10.5 | 21.5
Sporting Goods (451) | 55.4 | 52.3 | 54.2 | 30.7 | 29.1 | 21.2 | 14.0 | 18.7 | 24.6
Electronic & Appliances (443) | 30.3 | 31.0 | 29.5 | 34.1 | 27.1 | 24.9 | 35.6 | 41.9 | 45.6
Health Goods (446) | 49.0 | 50.0 | 46.8 | 19.0 | 21.3 | 20.5 | 32.0 | 28.7 | 32.6
Toys (451) | 40.7 | 27.6 | 22.0 | 45.2 | 47.7 | 46.9 | 14.1 | 24.7 | 31.1
Home Goods (444) | 63.9 | 72.8 | 72.4 | 17.2 | 11.6 | 10.9 | 18.9 | 15.6 | 16.6
Groceries (445) | 79.8 | 67.2 | 59.7 | 6.6 | 16.2 | 22.8 | 13.6 | 16.6 | 17.5
Average | 55.8 | 53.2 | 50.0 | 26.4 | 25.5 | 23.2 | 17.8 | 21.3 | 26.8

  * •

Notes: The numbers come from the Census of Retail Trade data. GM includes
stores in subsector 452. Other includes sales outside of the main subsector
(indicated in parenthesis) and GM. Average is the arithmetic mean of the
numbers in the column. (CBDRB-FY20-P1975-R8604)

####  D.2 Extended Sample

We now present results with an extended sample that covers the period 1982 to
2012. The 1982 and 1987 Censuses of Retail Trade do not include product-level
sales for all the categories we consider in our main sample (1992-2012). The
affected product categories, Toys and Sporting Goods, account for a relatively
small share of total retail sales. Therefore, we focus on results for the
retail sector as a whole which we believe are reliable for this time period.

Figure D.1: National and Local Concentration Notes: The data are from the
Census of Retail Trade. The Herfindahl-Hirschman Index (HHI) for four
different geographic definitions of local markets and national concentration
are plotted. The local HHI is aggregated using each location’s share of
national sales within a product category. The numbers are sales weighted
averages of the corresponding HHI in the product categories. (CBDRB-
FY20-P1975-R8604)

Figure D.1 presents measured concentration indexes for different definitions
of local markets and the retail sector as a whole going back to 1982. We use
the store-level NAICS codes imputed by Fort and Klimek ((2018) to identify
retail establishments prior to 1992. Relative to Figure 1 we also include a
measure of local concentration where markets are defined by Metropolitan
Statistical Areas (MSA). There are more MSAs than commuting zones (about 900
vs 722) and MSAs do not partition the U.S., omitting rural areas. In practice,
the measured concentration level for MSAs is similar to that of commuting
zones.

Extending our sample to 1982 does not change the main result of increasing
national and local concentration. All measures show sustained increases
between 1982 and 2002. Looking at the full sample highlights the change in the
rate of increase of national concentration after 1997 which contrasts with the
slow increase during the 1980s.

Finally, we extend the decomposition exercise of Figure A.1 to 1982. The
results, shown in Figure D.2, show a stark decrease in the contribution of
local concentration to national concentration. Even though the role of local
concentration was never large (always below 6 percent), the share of national
concentration attributed to local concentration fell sharply during the 1990s,
ending at roughly 2 percent in 2002.

Figure D.2: Share of Local Concentration Term in National Concentration Notes:
The numbers are from the Census of Retail Trade. The share of local
concentration is measured as the ratio of the local concentration term in
equation (5) to the national Herfindahl-Hirschman Index (HHI). We aggregate
the local concentration terms across the product categories using their sales
shares. (CBDRB-FY20-P1975-R8604)

####  D.3 Non-Store Retailer Additional Details

The penetration of non-store retailers varies widely across products. As
Figure D.3 shows, the sales share of non-store retailers is highest in
Electronics and Appliances, with an initial share of 7.5 percent in 1992 and a
share of 20.9 percent in 2012. The initial differences were large, with only
two categories (Electronics and Sporting Goods) having a share of more than 5
percent. By 2012, non-store retailers accounted for more than 15 percent of
sales in five of the eight major categories. Despite this widespread increase,
not all products are sold online. By 2012, only 0.7 percent of Groceries sales
and 3 percent of Home Goods sales were accounted for by non-store retailers.
These two categories account for almost half of all retail sales, which
explains the overall low sales share of non-store retailers.

Figure D.3: Non-Store Retailers Share across Product Categories Notes: The
numbers are the national sales shares of non-store retailers by product
category from the Census of Retail Trade microdata. (CBDRB-FY20-P1975-R8604)

Because the share of national sales going to non-store retailers is quite
small these retailers have almost no impact on national concentration numbers
until the 2000s. In Table D.2, we show national concentration numbers both
with and without non-store retailers. The trends are similar with non-store
retailers slightly lowering the increases in national concentration.

Table D.2: National HHI with and without Non-Store Retaliers

| 1982 | 1987 | 1992 | 1997 | 2002 | 2007 | 2012
---|---|---|---|---|---|---|---
Excluding Non-store | 0.0082 | 0.0103 | 0.0128 | 0.0184 | 0.0311 | 0.0418 | 0.0426
Including Non-store | 0.0083 | 0.0103 | 0.0124 | 0.0175 | 0.0286 | 0.0373 | 0.0391

  * •

Notes: The numbers come from the Census of Retail Trade data. The numbers in
the first row are the same numbers as in Figure 1 and represent the National
HHI excluding non-store retailers. The numbers in the second row include
establishments in NAICS 4541. (CBDRB-FY20-P1975-R8604 and CBDRB-
FY23-P1975-R10585)

####  D.4 Top 4 Firm Shares

Here we show that the average market share of the four largest firms in each
product and local market increases steadily during our sample for all
geographies larger than a zip code. We find the largest increases in commuting
zone and metropolitan statistical areas. The average share of the four largest
firms for zip codes increases until 2002 and then decrease over the next 10
years.

Table D.3: Average Top 4 Firm Share

| 1982 | 1987 | 1992 | 1997 | 2002 | 2007 | 2012
---|---|---|---|---|---|---|---
Commuting Zone | $0.35$ | $0.37$ | $0.38$ | $0.38$ | $0.41$ | $0.42$ | $0.42$
MSA | $0.31$ | $0.33$ | $0.34$ | $0.35$ | $0.38$ | $0.39$ | $0.39$
County | $0.43$ | $0.45$ | $0.45$ | $0.45$ | $0.47$ | $0.47$ | $0.46$
Zip | $0.70$ | $0.71$ | $0.72$ | $0.72$ | $0.72$ | $0.70$ | $0.68$

  * •

Notes: Results come from the Census of Retail Trade. The market share of the 4
firms with the greatest sales in each product category and location in each
year are summed. These results are then aggregated using a weighted average of
the sales share of each product and location in a year. (CBDRB-
FY20-P1975-R8604)

####  D.5 10 Year Concentration Changes

We now turn to the distribution of changes in concentration across markets. We
find that the increases in concentration have been broad based. Almost 60
percent of dollars spent in 2012 are spent in markets that have increased
concentration since 2002 (Figure 4(d)). In just 10 years, 23 percent of
markets have increases in concentration of over 5 percentage points (Figure
4(b)). These changes are significant. For comparison, the Department of
Justice considers a 2 percentage point increase in the local HHI potential
grounds for challenging a proposed merger ((Department of Justice and Federal
Trade Commission, 2010).

Figures 4(a) and 4(c) show that the changes in concentration were even more
widespread between 1992 to 2002. Over 69 percent of markets, accounting for 72
percent of retail sales, increased their concentration. In both the 1992–2002
and 2002–2012 decades, the majority of retail sales occurred in markets with
relatively small increases in concentration (between 0 and 5 percentage point
increases in the market’s HHI). These markets account for 66 percent of retail
sales in 2002 and 55 percent in 2012.

Figure D.4: Changes in Concentration across Markets

(a) Unweighted 1992–2002

(b) Unweighted 2002–2012

(c) Weighted 1992–2002

(d) Weighted 2002–2012

Notes: The numbers are based on calculations from the Census of Retail Trade.
The top panels show the fraction of markets, commuting zone/product category
pairs, with changes in concentration of a given size. The bottom panels weight
markets by the value of sales in the product category. The columns report
changes for the decades 1992 to 2002 and 2002 to 2012. (CBDRB-
FY20-P1975-R8604)

####  D.6 Industry-Based Results

This subsection provides more details on our industry based results. Figure
D.5 shows national and local concentration for eight retail subsectors
(3-digit NAICS). Local concentration is defined at the commuting zone level.
The increasing trends we documented for national concentration in the retail
sector are present in all subsectors, but the increase is particularly strong
for general merchandisers (NAICS 452) at both the national and at the local
level. The general merchandise subsector includes department stores, discount
general merchandisers, and supercenters. Over time a small number of firms
have come to dominate this format. Similar patterns arise in local
concentration. Figure 5(b) shows local concentration for the major subsectors,
calculated as a weighted average of the industries comprising each subsector.
Local industry concentration levels are higher than national and they also
increase.

Figure D.5: National and Local Concentration Across Industries

(a) National Concentration

(b) Local Concentration

Notes: The data are from the Census of Retail Trade. Numbers are the national
and local (commuting zone) Herfindahl-Hirschman Index (HHI) for various
industries weighted by market size. Concentration is calculated using 6-digit
NAICS codes and aggregated to the 3-digit NAICS using each industry’s share of
sales. (CBDRB-FY20-P1975-R8604)

####  D.7 The Relationship Between National and Local HHIs

This subsection presents the levels of the national HHI in the counterfactual
economy described in Section 4. Table D.4 presents the underlying numbers for
Figure 6.

Table D.4: Multi-Market Firms Counterfactual

| National HHI
---|---
| 1992 | 1997 | 2002 | 2007 | 2012
Actual HHI | 0.0128 | 0.0184 | 0.0311 | 0.0418 | 0.0426
Counterfactual HHI 1992 | 0.0128 | 0.0135 | 0.0158 | 0.0171 | 0.0161
Counterfactual HHI 1997 | — | 0.0184 | 0.0232 | 0.0249 | 0.0239
Counterfactual HHI 2002 | — | — | 0.0311 | 0.0354 | 0.0340
Counterfactual HHI 2007 | — | — | — | 0.0418 | 0.0404

  * •

Notes: The numbers are based on calculations from the Census of Retail Trade.
The table reports the level of the national HHI and its counterfactual levels
preserving the market structure of each Census year. The counterfactual values
are computed by preserving the rank of firms according to the initial market
structure, assigning to the firm with the $r^{th}$ largest shares in the
initial year the market share of the $r^{th}$ firm in each subsequent year.
(CBDRB-FY23-P1975-R10585)

###  Appendix E Comparison to Rossi-Hansberg, Sarte, and Trachter (2020)

This section compares our results to those in Rossi-Hansberg, Sarte, and
Trachter ((2021) (hereafter RST) for the retail sector and explains the
factors contributing to the differences between our papers. Unlike us, they
find a reduction in the local HHI for the retail sector between 1990 and 2014.
RST present results for many sectors of the economy. In what follows we
discuss only their results in the retail sector. However, our discussion of
aggregation methods is relevant for all sectors.

There are three key differences between our paper and RST’s that each
partially explains the opposite results regarding local concentration. First,
we use different data sources: while RST use the National Establishment Time
Series (NETS), this paper uses confidential data from the CRT and the LBD.
Second, we have different definitions of markets: this paper defines markets
by product based on NAICS-6 classification of establishments, while RST define
markets by industry based on SIC-8 or SIC-4 classification of establishments.
Third, we differ in the methodology used to aggregate markets. This paper
aggregates market-level concentration using contemporaneous weights, and we
report the change in this (aggregate) index of local concentration. In
contrast, RST aggregate the change in market-level concentration using end-of-
period weights and report this (aggregate) change.

We argue that the CRT is likely to provide better data for the study of
concentration in local markets, and we show that changing from NETS to CRT
data alone explains a third of the discrepancy in the change of local
concentration (while controlling for market definition and aggregation
methodology). Another third of the difference in estimates is explained by the
definition of product markets (by changing detailed SIC-8 industries to more
aggregated SIC-4 industries). The proper definition of a product market
(SIC-8, SIC-4, NAICS-6, product category) can depend on the question being
asked. We argue in Section 2.3 that product categories are the proper way to
study retail markets. The final third of the difference in estimates is
explained by the aggregation methodology. We argue that the method used by RST
is biased toward finding decreasing local concentration, and we show that
their method could find evidence of decreasing concentration in a time series,
even when concentration is not changing in the cross-section. This occurs when
markets become less concentrated as they grow. Below we expand upon these
differences and their implications for the measurement of local concentration.

##### Data sources

The baseline results in RST are based on the NETS, a data product from Walls
and Associates that contains information on industry, employment, and sales by
establishments. These data have been shown to match county-level employment
counts relatively closely ((Barnatchez, Crane, and Decker, 2017), but the data
do not match the dynamics of businesses Crane and Decker ((2020). The results
in this paper are based on the CRT, a data set assembled and maintained by the
U.S. Census Bureau covering all employer retail establishments.

Both the NETS data and the CRT use the establishment’s reported industry and
sales when available and both have some degree of imputation for
establishments that do not report. However, the CRT can often impute using
administrative records from the IRS.999Response to the CRT is required by law.
Single-unit establishments are randomly sampled for sales in the CRT, while
the non-sampled units have their sales imputed. See http://dominic-
smith.com/data/CRT/crt_sample.html for more details. Beyond this, the two data
sets differ in other two relevant aspects. First, the CRT contains sales by
product category for the majority of sales, while the NETS contains only
industry, allowing us to define markets by product categories and account for
cross-industry competition by general merchandisers (see Section 2.3). Second,
the NETS includes non-employer establishments, while the CRT does not.
According to official estimates, non-employer establishments account for about
2 percent of retail sales in 2012 (Economy-Wide Key Statistics: 2012 Economic
Census of the United
States).101010https://factfinder.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ECN_2012_US_00A1&prodType=table
On the whole, the CRT provides a more accurate picture of activity in the
retail sector.

##### Definition of product markets

We adopt a different definition than RST for what constitutes a product
market. Each definition of product market has its own pros and cons, and
researchers may choose one over the other depending on the specific context.
We define markets by a combination of a geographical location and a product
category that we construct using the detailed data on sales provided by the
CRT, along with the (NAICS-6) industry classification of establishments (see
Section 2.3). As we mentioned above, doing this treats multi-product retailers
as separate firms, ignoring economies of scope, in favor of putting all sales
in a product category in the same market. However, we also present results
defining markets by industry and find that the same patterns of higher
national and local concentration arise, but with stronger magnitudes. See
Section 3.4.

In contrast, RST define markets by the establishment’s industry, using both
SIC-8 and SIC-4 codes. Some examples of SIC-8 codes are department stores,
discount (53119901); eggs and poultry (54999902); and Thai restaurants
(58120115).111111NETS allows for 914 retail SIC-8 codes. A full list is
available at https://www.dnb.com/content/dam/english/dnb-solutions/sales-and-
marketing/sic_8_digit_codes.xls. RST indicate that many SIC-8 codes are rarely
used (data appendix), but without access to the NETS data, we cannot assess
the relative significance of each code for economic activity. SIC-8 codes may
be overly detailed for retail product markets, to the point that many
retailers will sell multiple types of goods. For example, calculating
concentration in eggs and poultry (54999902) would miss the fact that many
eggs and poultry are sold by chain grocery stores (54119904) and discount
department stores (53119901). This suggests that aggregating to less detailed
codes may provide a better definition of product markets. To that end, RST
present results for SIC-4 codes. When concentration is calculated using SIC-4
codes, the decrease in local concentration is much smaller, a 8 percentage
point decrease instead of a 17 percentage point decrease.121212The change from
SIC-8 to SIC-4 has little effect on concentration outside of retail (RST Data
Appendix). The numbers are read off graphs for the change in retail sector
concentration for zip codes between 1990 and 2012.

Incidentally, the SIC-4 codes are quite similar to the NAICS-6 codes available
in the CRT, except restaurants are included in the SIC definition of retail
but not in NAICS.131313In the results in the main text, we exclude automotive
dealers, gas stations, and non-store retailers because of concerns related to
ownership data and defining which markets they serve (see Section 2 for
further discussion). This has little impact on the estimates for local
concentration. This makes the concentration measures based on each
classification more closely comparable. Yet, even in this setting (NETS SIC-4
versus CRT NAICS-6) there are still significant differences between our
studies. We will go back to this comparison when we discuss Figure E.2 and
Table E.1 below.

##### Aggregation methodology

The final difference comes from how we aggregate the market-level changes in
concentration into an aggregate index of local concentration. We compute the
local HHI index by first computing the HHI for each pair of product category
$(j)$ and location $(\ell)$. Then we aggregate across locations, weighting
each market (location-product) HHI by the market’s share of the product’s
national sales. Doing this provides a measure of the average local HHI for
each product. Finally, we aggregate across products, weighting by the
product’s share of national retail sales, to obtain an average local HHI.
Every step in the aggregation maintains the interpretation of the HHI as a
probability, which also makes the levels of the HHI comparable across time. We
do this for each period $(t)$ and report the time series for this index. The
average local HHI is then given by

$\displaystyle
HHI_{t}=\underbrace{\sum_{j}s_{j}^{t}}_{Products}\underbrace{\sum_{\ell}s_{\ell}^{jt}}_{Locations}\cdot
HHI_{j\ell t},\quad\text{where }HHI_{j\ell t}=\sum_{i}\left(s_{i}^{j\ell
t}\right)^{2}.$ (E.1)

RST use a different methodology. Instead of computing concentration in the
cross-section, they calculate the change in concentration between $t$ and some
initial period and then aggregate these changes weighting by the period $t$
share of employment of each industry $(j)$ in total retail employment. Their
index for the change in concentration is given by141414Equation E.2 is taken
from RST, with notation adjusted to match the notation in this paper.

$\displaystyle\Delta HHI_{t}^{RST}=\sum_{j\ell}s_{j\ell}^{t}\Delta HHI_{j\ell
t},$ (E.2)

where $s_{j\ell}^{t}$ is the sales share of industry $j$ and location $\ell$
in the country at time $t$151515RST weight markets by their employment share
$\left(e_{j\ell}^{t}\right)$ instead of their sales share $\left(s_{i}^{j\ell
t}\right)$. However, their data appendix shows this has no effect on the
results. and $\Delta HHI_{j\ell t}$ is the change in the revenue-based HHI in
industry $j$ and location $\ell$ between the base period and time $t$.

The key difference between the methodologies is that RST do not account for
the size of a market in the initial period. This is shown in equation E.3,
which subtracts the two measures of concentration from each other. After
canceling terms, the difference between the two measures is

$\displaystyle\Delta HHI-\Delta HHI^{RST}$
$\displaystyle=\sum_{j\ell}\underbrace{(s_{j\ell}^{t}-s_{j\ell}^{0})}_{\Delta
s_{j\ell}^{t}}\cdot HHI_{m\ell 0}.$ (E.3)

RST will weight markets that increase in size over time by more in the initial
period, while those that decrease will be weighted less relative to our
measure. As markets grow, they typically become less concentrated resulting in
RST weighting markets with decreasing concentration more than markets with
increasing concentration.161616A similar point is made in Appendix E of
Ganapati ((2021) using LBD data.

Figure E.1 shows that this methodology can find decreasing concentration in a
time series, even when concentration is not changing in the cross-section.
Consider three firms (A, B, and C) that operate in two markets and have the