Cities and Product Variety
Nathan Schiff∗
July 2012†
Abstract
This paper measures horizontal differentiation in the restaurant industry and suggests that city structure directly increases product variety by spatially aggregating demand. I discuss a model of entry thresholds in which market size is a function of both population and geographic space and then evaluate implications of this model with a new data set of 127,000 restaurants across 726 cities. I find that the
geographic concentration of the population leads to a greater number of cuisines and that the likelihood
of having a specific cuisine is increasing in population density with the rarest cuisines found only in the
densest cities. Further, there is a strong hierarchical pattern to the distribution of variety across cities in
which the specific cuisines available can be predicted by the total count.
1
Introduction
Easy access to an impressive variety of goods may be one of the most attractive features of urban living. Economists have long argued that consumers have a love of variety (e.g. Dixit and Stiglitz 1977)
and more recent work in urban economics suggests that consumption amenities, especially local or nontradable goods, are a significant force driving people to live in cities (Glaeser, Kolko, and Saiz 2001, Chen
and Rosenthal 2008, Lee 2010). The amount of product variety in a market may also provide insight
into the intensity of competition as firms in differentiated markets may face less direct price competition
(Mazzeo 2002). Despite the potential importance, we have little evidence on product variety in cities and
therefore cannot explain why some cities seem to have more variety than others. In this paper I provide
the first systematic measurement of product variety across a large set of cities for an important non-tradable
consumption amenity–restaurants–and show that a simple model of demand aggregation can explain a great
deal of the variation across locations. I will argue that large, dense cities concentrate groups of consumers
with the same preferences in a small geographic space, thus providing the necessary demand for a restaurant
catering to that taste. Using a unique data set of over 127,000 restaurants across 726 US cities I find that for
large cities it is not just the population size and demographic characteristics but also the city’s land area and
the geographic clustering of specific populations that affect the amount of product variety in a city. For the
∗ Assistant
Professor, Sauder School of Business, University of British Columbia [email protected]
paper stems from work on my PhD thesis and I thank my advisers Nathaniel Baum-Snow, Vernon Henderson, and Brian
Knight for much appreciated advice and support. I also thank Kristian Behrens, James Campbell, Tianran Dai, Tom Davidoff,
Andrew Foster, Martin Goetz, Juan Carlos Gozzi, Toru Kitagawa, Sanghoon Lee, Mariano Tappata, Norov Tumennasan, seminar
participants at Brown University, the Center for Economic Studies at the Census Bureau, the Sauder School at UBC, the Federal
Reserve Bank of Philadelphia, and conference participants at the CUERE 2011, IIOC 2009, and NARSC 2009 and 2011 for
helpful comments.
† This
1
182 cities in the top quartile by land area of my data (mean population 331,000), a one standard deviation
increase in log population is associated with a 57% increase in the count of unique cuisines. A one standard
deviation decrease in log land area–which increases population density without changing the size of the
population–is associated with a 10% increase in cuisine count, equivalent to increasing the percentage of
the population with a college degree by one standard deviation and larger than the effect of increasing the
ethnic population associated with each cuisine by one standard deviation. For the smallest cities in land area
I find that population alone is the most important factor and estimate that a one standard deviation increase
in log population is associated with a 145% increase in cuisine count but that changing land area to increase
density would have little effect.
In their “Consumer City” paper, Glaeser, Kolko and Saiz (2001) write that there are “four particularly
critical amenities” leading to the attractiveness of cities and that “first, and most obviously, is the presence
of a rich variety of services and consumer goods.” Noting that most manufactured goods can be ordered and
are thus available in all locations, they write that it is the local non-tradable goods that define the consumer
goods of a city. I will continue with this notion of local non-tradable consumer goods and suggest that it is
especially for products characterized by significant consumer transportation costs, heterogeneous tastes, and
a fixed cost of production, that the ability of cities to agglomerate people with niche tastes will lead to greater
variety. Examples of this type of product would include bars, concert halls, hair salons, movie theaters,
museums, restaurants and any other location-based service or good that is differentiated and patronized by
consumers with a specific set of preferences. This idea would also hold for retailers that aggregate specific
collections of tradable goods and where visiting the store itself provides some benefit to the consumer, such
as specialty bookstores, niche toy stores, or clothing boutiques.
Theoretical models of product differentiation almost always specify that each firm produces a unique
product, such as in Dixit-Stiglitz models with CES utility, circular city models, or discrete choice models
(Dixit and Stiglitz 1977, Salop 1979, Anderson, de Palma, and Thisse 1992). Additionally, product varieties
are often assumed to be symmetric in that every variety is valued equally by the consumer, making only the
count of varieties important and not the actual labels or identities of the products1 . While this view of variety
has been quite useful in tackling many economic problems2 , I believe it is not appropriate for characterizing
variety as described in the consumer cities literature. When variety is discussed as a consumption amenity
it usually implies a range or count of product sub-categories3 ; a city with five hamburger restaurants has
less variety than a city with one hamburger restaurant and four other restaurants serving French, Italian,
Chinese, and Mexican cuisines. Furthermore, casual observation indicates that larger cities tend to have
specialized or rarer varieties that are not found in smaller cities. In order to quantify and explain any patterns
in the distribution of varieties across cities it’s necessary to identify the specific labels of these varieties; a
symmetric framework would ignore many possible patterns.
However, this categorization approach to variety is difficult to use empirically. While data on tradable
goods often has quite granular categorization (e.g., SITC codes), the data on non-tradable consumption
amenities seldom has precise information on characteristics of the goods; further, it might not even be clear
what is the appropriate classification scheme. For this reason restaurants are particularly well suited to
the aims of this paper. Product differentiation is easily measured: restaurant varieties can be identified by
cuisine and this categorization is fairly uncontroversial4 . Moreover, transportation costs are often significant
1 Here
I use the wording of Dixit-Stiglitz to describe symmetry. They discuss an asymmetric case of their model in chapter 4
of the compilation ”The Monopolistic Competition Revolution in Retrospect” (Brakman and Heijdra 2004).
2 One prominent example is the new economic geography, see (Fujita, Mori, Henderson, and Kanemoto 2004).
3 Glaeser, Kolko, and Saiz (2001) describe variety as a ”range” of services” and ”specialized retail”; Lee (2010) notes that
”large cites have museums, professional sports teams, and French restaurants that small cities do not have.”
4 Obviously there is some flexibility in categorization but for the purpose of this paper it doesn’t matter whether a restaurant is
classified as Southern Italian or Italian as long as the categorization schema is consistent across cities.
2
Figure 1: Restaurants and Cuisines vs Population
8
6
4
2
0
0
2
4
6
8
10
Cuisine Count ((log)
g)
10
Restaurant Count ((log)
g)
8
10
12
14
Pop 2007-8 (logs)
Log #Restaurants
#
16
8
Fitted values
10
12
14
Pop 2007-8 (logs)
Log #Cuisines
#C
((m1))
Slope=1.01, RSq=.86, results for 726 Census Places
16
Fitted values
Slope=.49, RSq=.67, results for 726 Census Places
in the decision to eat at a restaurant5 , a factor that could make the variety in cities different from that in
places with more dispersed populations. Finally, there exists a wealth of information about restaurants on
the Internet, including precise address information allowing accurate geographic matching of firm counts to
demographics data.
The difference between the firm count and categorization approach to variety can be readily seen in
Figure 1. The left-hand panel plots the number of restaurants against population for the cities (Census
Places) in my data set and shows a clear log-linear pattern with a slope very close to one. This result
was also found in (Berry and Waldfogel 2010) and (Waldfogel 2008) using different data and illustrates a
strong proportional relationship between population and restaurant count. The right-hand panel shows the
count of cuisines plotted against population for the same cities and displays a very different pattern with far
more variance. Explaining this pattern and showing the importance of both consumer characteristics and
geography will be the focus of much of this paper.
1.1
Related Literature
This paper is related to a large literature on market size and firm characteristics. Syverson (2004) proposes
a model in which large markets with many producers allow consumers to easily switch their patronage,
thus increasing competition and leading to more efficient firms–a result borne out in the author’s data on
the concrete industry. Campbell and Hopenhayn (2005) investigate the link between market size, average
revenue, and average employment, and also conclude that competition is tougher in larger markets. Notably,
they find that ”eating places,” defined as places to eat with and without table service, have larger average
size and greater dispersion of sizes in larger markets. The authors use population and population density as
alternative measures of market size but find that their results are roughly the same. While this would seem
to downplay the importance of space in market measurement their data set does not include any measures
of horizontal differentiation. In my paper I will set aside the issue of firm efficiency and instead focus on
5 Intuitively,
consumers are not willing to travel very far for a meal, as evidenced by the large number of identical fast food
franchises in the same city.
3
how market size affects differentiation, making the assumption that efficiency does not affect the degree of
horizontal differentiation.
Berry and Waldfogel (2010) study vertical differentiation, or differentiation in quality, and contrast the
effect of market size in industries where quality is produced with fixed costs (e.g., newspapers) to industries
where quality is produced with variable costs (e.g., restaurants). In industries where quality is tied to fixed
costs, increasing market size allows a high quality firm to undercut lower quality firms and thus the market
remains concentrated with just a few high quality firms. On the other hand, if quality is produced with
variable costs then higher quality firms cannot undercut lower quality competitors and larger markets will
show a greater range of available qualities. The authors find that higher quality restaurants are found in
bigger cities, similar to my finding that relatively rarer restaurants are found in bigger cities. Apart from
this similarity, it is rather difficult to compare their results on vertical differentiation to mine on horizontal
differentiation6 .
Two recent papers consider horizontal differentiation in the restaurant industry and look at the effects
of specific populations on the cuisines of local restaurants. Waldfogel (2008) combines several datasets,
including survey data on restaurant chain consumers, to show that the varieties of chain restaurants in a
zip code correspond to the demographic characteristics of the population. Mazzolari and Neumark (2010)
use data on restaurant location and type in California combined with Census data to show that immigration
leads to greater diversity of ethnic cuisines. This paper will also advance an argument about the importance
of clustered groups with a particular taste but differs in subject and aim from these papers in several important ways. First, while Waldfogel is interested in showing the relationship between restaurant type and
demographics at a zip code level and Neumark looks at commuting-defined markets in California, this paper
will focus on the city level and use a national set of data. I can then make general statements about cities
and variety and tie my findings to the urban and trade literatures on cities, such as Central Place Theory
and the New Economic Geography. Second, while Waldfogel looks specifically at fast food restaurants and
Neumark at a larger set of mostly ethnically-defined restaurants, I will use data covering all restaurants with
very precise categorization (90 cuisines or 450 cuisine-price pairs) so that I can provide a general measure
of product diversity for a city. Finally, I develop a model to formalize how entry thresholds are affected by
population and space. While this model is quite simple, it allows me to show how the product diversity of a
city fluctuates with changes to overall city density. For these reasons I view this paper as complementary in
that I provide further evidence of the role of specific preference groups in the location choice of corresponding firms7 but extend this finding to a general theory of demand aggregation that helps to explain why cities
differ in the variety of these goods they offer.
2
Population, Land Area, and Entry
The essence of my argument is that given positive transport costs there must be enough demand in a small
enough space to support a given variety. This general idea is straightforward and was mentioned in the
context of restaurants in both Glaeser, Kolko, and Saiz (2001) and Waldfogel (2008). Glaeser, et. al. note that
6 In
vertical differentiation models all consumers agree upon standards of quality and quality differences across firms often
stem from differences in costs or efficiency. Horizontal differentiation views all firms as equals that cater to different parts of the
consumer taste distribution, meaning quality would not be an appropriate measure of horizontal differentiation. Additionally, the
authors focus on the availability of high quality restaurants in different markets, limiting their data to the restaurants appearing in
the Mobil and Zagats guides, while I am concerned with the entire range of cuisines, but not quality.
7 Both my paper and Waldfogel discuss a demand-driven explanation but Mazzolari and Neumark (2010) argue that the supplyside, through comparative advantage in ethnic restaurant production, is the more important channel through which local ethnic
groups lead to local ethnic restaurants.
4
“the advantages from scale economies and specialization are also clear in the restaurant business where large
cities will have restaurants that specialize in a wide range of cuisines--scale economies mean that specialized
retail can only be supported in places large enough to have a critical mass of consumers.” Waldfogel writes:
“some products are produced and consumed locally, so that provision requires not only a large group favoring
the product but a large number nearby.” While this demand-side argument is intuitive it is still not clear what
defines a critical mass and how entry might be affected by markets with different populations and land areas.
Markets with large populations in small areas offer firms greater access to consumers but they may also
face greater competition and thus lower markups. Implicitly, a critical mass is a concept about population
density but is density sufficient for making predictions about entry or does the effect of density depend
upon the geographic area of the market? To address these and other issues I will use Salop’s circular city
model of monopolistic competition but rather than normalizing population and land to one I keep these as
separate parameters. To this model I introduce the idea of an entry threshold in the spirit of (Bresnahan
and Reiss 1991)8 to define the minimum conditions that would allow the first firm of a given type to enter
the market and I allow firms of different types to face different thresholds for entry. I then map these entry
thresholds in population and land space to show how product variety will be affected by different market
sizes.
I will be discussing a market in which firms are differentiated by both product type and location, and
must choose a price given a market with free entry and positive transportation costs. If firms differentiate
by both type and location then consumers may value different configurations of firm locations and types
equally. For example, a consumer may be indifferent between their preferred variety at one distance and
a lesser-preferred variety at a shorter distance. This trade-off between distance and type could result in
multiple equilibria or imply the non-existence of an equlibrium9 . In order to make the model tractable I
make the strong assumption that firms of different types don’t compete or in this context, that restaurants
of different cuisines don’t compete. While this is clearly unrealistic, I believe that the intuition gained from
this model still holds for several reasons. First, the idea that there must be a minimum number of consumers
in a small enough space to allow entry of a given type must hold with and without inter-type competition10 .
Second, the assumption of no competition across types can be viewed as an extreme form of the assumption
that firms of the same type compete more closely with each other than with other types. In this paper I am
interested in simply showing that there must be a minimum number of consumers in a small enough space
to permit a firm of that type to exist, and I do not try to predict the count of restaurants in each cuisine for
each city11 nor within city location patterns12 . Narrowing my aims to this objective allows me to make the
8 Bresnahan
and Reiss (1991) develop a model of entry thresholds in which a market must satisfy specific conditions in order
to permit entry of each successive firm in an industry (from monopolist to perfect competitor).
9 Salop specifies a symmetric, zero profit equilibrium where firms are equally spaced and all earn zero profit. If there are
multiple types and asymmetric competition, meaning that a firm of one type competes more strongly with firms of the same type
than with firms of other types, then this equilibrium often can’t exist. For example, there can not be an even number of firms of
one type and an odd number of firms of another type since some firms would have different neighbors and face more competition,
and thus profit cannot be zero for all firms.
10 Consider a market where there are two types of firms, consumers like both types, but all consumers prefer one type to the
other. When two asymmetrically-differentiated firms compete the greater-preferred firm always has an advantage over the lesserpreferred firm, and thus demand conditions must be quite favorable for the lesser-preferred firm to exist. I will show that even
without competition across types, a market must have a minimum population, which varies with land area, in order to sustain any
given type. Therefore allowing competition between firms simply makes it even more difficult for a lesser-preferred firm to exist.
11 Mazzeo (2002) develops a model of oligopoly where firms make entry and product quality decisions simultaneously and
estimates the distribution of motels across quality types for small exits along US highways. Unfortunately this model is less
relevant to the monopolistically competitive restaurant industry where simultaneous entry of thousands of differentiated firms
seems a very strong assumption. Further, while Mazzeo looks at markets with a small number of motels across three quality types,
the markets in my dataset have thousands of restaurants with up to 82 cuisines, making estimation intractable.
12 In their theoretical paper Irmen and Thisse (1998) show that when duopolists compete in multiple dimensions they will choose
5
strong assumption that firms of different types don’t compete.
An alternative supply-side argument would suggest that specific types are only found in cities with restaurateurs of that type. However, the supply-side explanation alone is not very convincing: if there is significant
demand in a city for a specific type than a restaurateur of that type should move to the city. I therefore focus
on providing evidence for this critical mass argument but discuss this alternative explanation at the end of
my empirical section when looking at the clustering of ethnic populations.
2.1
Entry Threshold for a Single Firm
I will use the classic Salop circular city model to derive minimum conditions of population and land area that
allow entry (see appendix for a brief discussion integrating my results with Salop’s paper). In Salop’s model
(Salop 1979) consumers are located uniformly around the perimeter of a circle and must decide whether
to purchase a good from a firm or consume their reserve good. Firms also locate around the perimeter of
the circle and can enter the market freely. Consumers are utility maximizers and receive utility u1 from the
firms’ product and utility u0 from the reserve good. There is positive transportation cost per unit distance, τ,
and thus a consumer located at l ∗ will purchase from a firm located at li with product price pi only if the net
utility of this transaction is higher than the consumer’s reserve utility.
max[u1 − τ∣li − l ∗ ∣ − pi , u0 ]
(1)
This paper is concerned with entry and thus I focus on the case of a single firm deciding whether to enter
the market, a potential monopoly’s entry problem. A consumer will only purchase from this firm if the price
and transportation cost are low enough. Define d as the distance that would make a consumer indifferent
between the firm’s good and their reserve utility:
u1 − τ ∗ d − p = u0
(2)
Solving through yields:
u1 − u0 − p
(3)
τ
From the firm’s perspective, the geographic extent of their market is the sum of the distances to the indifferent
consumer on either side of the firm: g = 2 ∗ d. We then have:
d=
u1 − u0 − p
τ
τg
p = u1 − u0 −
2
g = 2∗
(4)
(5)
Demand for the firm’s product is the geographic extent multiplied by the population density, D = NL . The
firm must pay a fixed cost F to enter and then produces the good with constant marginal cost c, making
profit:
(
)
τg
Π = u1 − u0 − − c Dg − F
(6)
2
to maximally differentiate in one dimension and minimally differentiate in all other dimensions. It is tempting to try and apply
this result to the context of restaurant locations but for several reasons the industry is not a good fit. As noted above, cities have
thousands of restaurants and Tabuchi (2009) shows that once there are three or more firms this max-min result no longer holds.
Further, restaurant consumers are not uniformly distributed in location or characteristics space, consumer tastes themselves do
not fit easily into a continuous space (how different is Italian from Japanese?), and restaurants enter markets sequentially over
long periods of time making current location patterns path dependent. Studying location choice with product differentiation in the
restaurant industry is a fascinating topic but beyond the scope of this paper.
6
The monopoly will choose the geographic extent that maximizes profit, which I will refer to as L∗ :
g∗ =
u1 − u0 − c
≡ L∗
τ
(7)
If the profit-maximizing geographic extent is actually larger than the total market area, L∗ > L, the monopolist will sell to the whole market, g = L. By writing average revenue, marginal revenue, and marginal cost
as a function of g I can show the monopolist’s problem of choosing the geographic extent graphically in
Figure 213 . The quantity sold is q = Dg, and thus density is just a scaling factor for these three functions
that does not affect the monopolist’s choice of g. I scale the vertical axis by density, making the units D$ , in
order to show the problem for any density. In the left hand panel of Figure 2 the horizontal axis shows the
Figure 2: Geographic Extent and Minimum Density
Population Density HNLL
$D
u1-u0
A
B
ACAHgL
ACBHgL
MRHgL
2N *L*
ARHgL
MCHgL
L*2
L*
1.5L*
2L*
Full Coverage
Market Extent HgL
L*2
(a) Monopolist Choice of Geographic Extent
Partial Coverage
L*
3L*2
Land Area HLL
2L*
(b) Minimum Density Given Land Area
monopolist’s choice of g. If the market area is large enough, L∗ ≤ L, the monopolist chooses g = L∗ where
the marginal revenue curve intersects marginal cost. If L < L∗ the monopolist is constrained and chooses
g = L; this case is analogous to a monopolist choosing quantity with a capacity constraint. I define “full
coverage” as the situation where the single firm sells to every consumer in the market, or g = L, and “partial
coverage” as when the firm sells to a subset of consumers, g = L∗ < L. The two cases converge at L = L∗
since the monopolist chooses g = L∗ . Given the monopolist’s choice of g, the necessary condition for entry
is that profit is weakly greater than zero. I consider the boundary case where profit is equal to zero—the
minimum condition for the first firm to enter—and write average revenue and average cost in terms of g:
(
τg )
F
AR(g) = AC(g) : D u1 − u0 −
= Dc +
2
g
F
(
)
D =
g u1 − u0 − c − τg
2
(8)
(9)
Equation 9 yields a unique density for every g: this is the minimum density in the market that would allow
the first entrant. Point A in Figure 2 shows an average cost curve drawn for the level of density that would
13 Average
(
)
revenue is AR(g) = D u1 − u0 − τg
2 , marginal revenue is MR(g) = D (u1 − u0 − τg), and marginal cost is MC(g) =
Dc.
7
make the monopolist’s profit equal to zero for geographic extent L∗ /214 . Point B shows the average cost
curve for g = L∗ , and is tangent to average revenue since marginal revenue is equal to marginal cost at L∗ .
Incorporating the monopolist’s choice of g given the city’s land area L, I plot the population density that
makes profit equal to zero against L in the right hand panel of Figure 2. It can be seen that the required
density decreases monotonically until reaching a minimum at L = L∗ . If the monopolist were to choose a
market extent g > L∗ the required density would actually increase since marginal profit is negative. However,
for all L > L∗ the monopolist chooses g = L∗ and thus the required population density is constant for markets
with area greater than L∗ . This constant density can be defined by a particular expression of population as
a ratio of the fixed cost, the difference between utility from the firm’s good and the reserve good, and the
marginal cost:
F
F
= ∗
(10)
N∗ =
u1 − u0 − c τL
∗
The constant density for markets with land area of L∗ or greater is thus D = 2N
L∗ . By rearranging equation 9
N
and substituting L for D I can write the expression giving the minimum population required for entry as a
function of land:
2N ∗ L∗ L
Nmin (L) =
(11)
g(2L∗ − g)
Adding the firm’s choice of g as a function of the market’s land area yields:
⎧ ∗ ∗
2N L
∗

⎨ 2L∗ −L if L ≤ L , ”full coverage”
Nmin (L) =

⎩ 2N ∗ L
if L∗ < L, ”partial coverage”
L∗
(12)
When land area is equal to zero, L = 0, the minimum population is N ∗ while when L ≥ L∗ then the population
∗
must be large enough such that the density is always D = 2N
L∗ . In the left-hand panel of Figure 3 the bottom
line, “Nmin (L; n = 1)”, shows the minimum population as a function of land area, with the break in the
function at L = L∗ . In the same panel I have also drawn the minimum population frontiers for n = 2 and
n = 3 firms15 . As noted earlier, the focus of this paper is on the extensive margin–when does a market have
a given variety–but I draw the frontiers for 2 and 3 firms to show how the minimum conditions derived hold
for markets with multiple firms. For markets with large land areas and populations just below the frontier,
such as a market with L = 3L∗ and N = 6N ∗ − ε, the model suggests that a small increase in population
would allow the market to go from having zero firms to three firms. What this shows is that while the count
of firms can change dramatically with small changes in population or land area, the extensive margin is still
governed by the minimum population frontier.
2.2
Population, Land, and Variety
To investigate variety across markets I introduce heterogeneous consumers with heterogeneous tastes. Denote the universe of varieties as v = 1...V , the markets as m = 1...M, and different population subgroups as
s = 1...S where a group could be defined by demographic characteristics like ethnicity, income, or education.
These groups are mutually exclusive so that the population of a market, Nm , can be completely partitioned
F
.
cost is plotted on the $/D scale and thus the curve plotted is average cost divided by density: c + Dg
multiple firms there are three possible equilibria for a given number of firms, depending upon the land area. These
conditions follow directly from (Salop 1979)–see Appendix for a short explanation rewriting his equations in my framework.
14 Average
15 With
8
Figure 3: Minimum Market Conditions: Land, Population
Minimum Population
Minimum Population
NminHL; n=1,∆=.1L
NminHL; n=2L
6N *
9N *2
3N *
2N *
N*
NminHL; n=1,∆=.2L
NminHL; n=3L
N .1
NminHL; n=1L
L*2
A
B
NminHL; n=1,∆=.5L
*
L* 4L*3
No entry
5L*2
2L*
3L*
N *.2
N *.5
Land Area
(a) Multiple Firms
L*2
3L*2
L*
2L*
Land Area
(b) Multiple Types
S
into the set of groups S: Nm =
∑ Nms. Further, let each group have a group-specific affinity for variety v, de-
s=1
noted βsv , which can be thought of as the percentage of people in that group who like variety v. Importantly,
I maintain the assumption of zero competition across types by assuming these βsv are exogenous so that
the demand for variety i in market m does not depend on the price or availability of variety j. The relevant
population for variety v in market m is then the sum of the different population subgroups weighted by their
S
subgroup-specific affinities:
∑ βsv ∗ Nms. I divide this weighted population by the population of the market
s=1
S
to get the percentage of consumers in market m who like variety v: δmv =
Nms
∑ βsv ∗ Nm . I again assume that
s=1
consumers of all groups are located uniformly throughout the perimeter of the circle.
To show how a heterogeneous population affects variety it is useful to start with the simplest case where
all markets have the same demographic profile such that the proportion of people in each group does not
= ξs , ∀m ∈ M. This condition implies that the percentage of people who like variety v
vary across cities, NNms
m
is the same in all markets: δmv = δv . I will also initially assume variety specific affinities are the same across
groups, βsv = βv . All firms, regardless of type, have the same fixed cost F and marginal cost c and thus have
the same minimum population required for entry, given a land area16 . If the market has Nm consumers but
only δv percent can potentially consume product type v then the minimum conditions for a firm of type v to
enter the market become:
⎧ 1 2N ∗ L∗
∗

⎨ δv ∗ 2L∗ −L if L ≤ L , ”full coverage”
Nmin (L; δv ) =
(13)

⎩ 1 2N ∗ L
∗
if L < L, ”partial coverage”
δv ∗ L ∗
Under these assumptions, I can rank varieties by the percentage of consumers who prefer the variety, δv .
In order for a firm to enter a market and sell a low δv variety the market must have a relatively higher
16 Empirically,
the fixed cost of opening a restaurant may vary across markets but as long as that cost is the same for different cuisines then the predictions of the model will be qualitatively unchanged. Also, as noted before, there is a strong linear
relationship between population and the number of restaurants in a market.
9
population and relatively smaller land area. Further, the minimum population required for less-preferred
varieties increases faster in the amount of land in a city:
⎧ α L∗
if L ≤ L∗ , ”full coverage”
 ∗v 2
∂ Nmin (L; δv ) ⎨ (2L −L)
(14)
=

∂L
⎩ 2N ∗
∗
δv L∗ = αv if L < L, ”partial coverage”
The right-hand panel of Figure 3 provides an example of mapping varieties to markets in land-population
space. In the figure, market A has three varieties while market B only has one variety, despite having a larger
population. The number of varieties is increasing to the north and west, although this is dependent upon
where the boundary lines are. Holding land constant, more populous markets will have more varieties and
holding population constant, smaller geographic markets will have more varieties, given that the city is
above the minimum population threshold. Figure 3 also suggests a highly hierarchical relationship between
the number and composition of varieties found in a market. Specifically, if market i has more varieties than
market j then market i will have all of the varieties found in market j; if a market has more varieties than
another it is because it can support the less-preferred (smaller δv ) varieties.
More formally, since the frontiers cannot cross—Nmin (L; δi ) > Nmin (L; δ j ) if δi < δ j —I can define each
∗
frontier uniquely by its population intercept, Nδv . Each market can then be defined by the intercept of the
frontier that would pass through the market’s location in land-population space, Im . Since each intercept can
∗
be interpreted as Nδv , this v is the variety preferred by the smallest percentage of people that market m can
support (whether or not a variety preferred by that percentage of people actually exists). For example, in
Figure 3 market B is on a frontier between the first and second varieties and has an intercept between N ∗ /.5
and N ∗ /.2. Generally, for markets m and l, if Im > Il ⇒ #Varietiesm ≥ #Varietiesl where the weak operator
stems from the fact that with discrete varieties a higher frontier may still not be high enough for the next
variety threshold. I can use this relationship to make ordinal statements about how population and land affect
the number of varieties in a market.
)
(
Nm L∗
Lm
1(L∗ < Lm )
(15)
#Varietiesm ∼ Im = Nm 1 − ∗ 1(Lm ≤ L∗ ) +
2L
2Lm
Specifically (and dropping subscripts):
(
)
∂ #Varieties
L
L∗
∼
1 − ∗ 1(L ≤ L∗ ) + 1(L∗ < L) > 0
∂N
2L
2L
∗
∂ #Varieties
−N
−NL
∼
1(L ≤ L∗ ) +
1(L∗ < L) < 0
∗
∂L
2L
2L2
(16)
(17)
The first equation shows that the count of varieties is increasing in population while the second equation
shows the variety count decreasing in land area. The ability to make ordinal statements about the count
of varieties stems directly from the hierarchical relationship. If I relax the equal subgroup proportions
assumption so that NNms
∕= ξs , ∀m ∈ M but maintain equal subgroup-variety affinities, βsv = βv , then there will
m
still be a strict hierarchy of varieties across markets. The percentage of consumers who like a given variety
S
Nms
will now vary across markets due to differing demographic profiles, δmv = βv ∑
, but the equal varietys=1 Nm
group affinities imply that if market m has variety i it must also have all varieties v where βv < βi , ∀v ∈ V .
However, relaxing the second assumption to allow group specific affinities for a variety will break down the
S
Nms
hierarchical relationship. With group-variety affinities, δmv = ∑ βsv ∗
, a market m will have variety v
Nm
s=1
10
if:
[(
δmv ∗ Nm
)
( ∗ )
]
L
Lm
∗
∗
1(L < Lm ) > N ∗
1 − ∗ 1(Lm ≤ L ) +
2L
2Lm
(18)
Consider markets A and B, varieties 1 and 2, and without loss of generality, let each market have land
area of zero so that a market m will have a specific variety v if δmv ∗ Nm > N ∗ . With group-variety affinities it
is now possible that δA1 NA > N ∗ , δA2 NA < N ∗ and δB1 NA < N ∗ , δB2 NA > N ∗ . As an example, we could think
of two cities where one city has a high percentage of people from ethnicity group 1 and the other city has
a high percentage of people from ethnicity group 2, both groups have high affinities for their corresponding
cuisines, and thus each has a restaurant catering to people from these groups. In other words, if tastes for a
given variety vary across demographic groups and demographic profiles vary across markets the hierarchical
relationship will break down and it will no longer be possible to make general statements about the count of
varieties. Nonetheless, equation 18 shows that controlling for the distribution across population subgroups,
it is still true that markets with greater populations and smaller land areas are more likely to have a given
variety.
To summarize, the theory offers the following predictions:
1. Controlling for demographics, the existence of a variety in a market can be determined by an entry
threshold in land-population space where the intercept is higher and the slope steeper for less-preferred
varieties
2. For a given variety and demographic profile, more populous markets and smaller geographic markets
are more likely to have the variety
3. Further, given enough similarity in the demographic profiles across markets there will be a hierarchical
relationship between the number of varieties and the composition of those varieties
3
Product Variety Across Cities
3.1
Data Collection
In order to study the relationship between market characteristics and product differentiation, one needs a
data source that satisfies several requirements. First, there must be a consistent categorization of firms into
varieties. Second, the data set must be exhaustive; if there is only data on select firms in the market then it is
not possible to compare counts of variety across markets. Third, the data set must have precise geographic
information on locations so that firms can be matched with the appropriate data on market characteristics.
Finally, the data set must cover a sufficient number of markets to allow comparisons across markets. These
requirements rule out the use of restaurant guides (not exhaustive, only cover a few markets) and information
directories or yellow pages (inconsistent categorization of types). The online city guide Citysearch.com has
exhaustive listings and covers many US cities17 . Additionally, while the same restaurant may be listed under
multiple cuisine headers, the actual entry for that restaurant lists one consistent, unique cuisine. Furthermore,
the entry for the restaurant also lists an exact street address. This allows me to avoid the difficulty of
reconciling census city boundary definitions to the boundary definitions used by the site in order to find the
appropriate city demographic (Census) information. In the spring of 2007 and the summer of 2008 I used a
software package and custom programming to download all the restaurant listings for the largest cities listed
on the site.
17 When
I collected my data this website appeared to be the most popular of its type; today Yelp.com has many of the same
features and seems to be more prominent.
11
I attempted to collect data for the 100 most populous US Census places and ended up finding 88 Citysearch cities matching these Census places. However, the Citysearch definition of cities often extended
far beyond the Census place geography. For example, the listing for “Los Angeles” included restaurants
in the Census places for “Beverly Hills,” “Long Beach,” “Santa Ana,” “Santa Monica” and many smaller
cities. Since I will be using demographic data to explain characteristics of a city’s restaurant industry it’s
important that my data for each city is fairly complete. In order to gauge how close the Citysearch data
was to the complete set of restaurants for every Census place I matched the count of Citysearch restaurants to the count found in the 2007 Economic Census, combining the categories “Full Service Restaurants”
(NAICS 7221) and “Limited Service Eating Places” (NAICS 7222). While close to the Citysearch types of
restaurants, the Economic Census includes some restaurants not always covered by Citysearch data, such
as fixed location refreshment stands, and therefore I expect that the Economic Census will record more
restaurants for every Census place than Citysearch. I define the ”match ratio” for each Census place as
#CitySearchRestaurants
and keep all Census places with a match ratio between .7 and 1.1,
MatchRatio = #EconomicCensusRestaurants
leaving 726 Census Places18 .
I categorize each restaurant with two separate cuisine measures. I denote the cuisine alone as “cuisine
measure 1” (ex: Italian, Ethiopian) and denote “cuisine measure 2” as the cuisine-price pair (ex: Italian 1$,
Ethiopian 2$) where the price can range from 1$ to 4$. Overall, about 35% of the restaurants have price data
and in defining cuisine measure 2 (m2) I break up each cuisine into 5 subgroups: one subgroup for each of
the four price levels and another if the price is missing. Given the fill rate and coarseness of these prices I
will concentrate mainly on the m1 measure and use the m2 measure as additional evidence. In Table 10 I
list all the cuisines and the count of cities in each land quartile with that cuisine. The rarest m1 cuisines are
Armenian and Austrian, found in just two cities19 while there are a number of cuisines found in every or
nearly every city (Chinese, Deli, Fast Food, Italian, Mexican, Pizza). The rarest m2 cuisines do not always
correspond to m1; for example “Caribbean” restaurants are found in 96 cities but only 3 cities have a 4$
Caribbean restaurant.
Table 1 shows summary statistics for the 726 cities by land quartile. Both cuisine measures are larger
for geographically bigger cities as well as the count of restaurants. The demographic characteristics, with
“Young” and “Old” categorizations following Berry and Waldfogel (2010), are quite similar across land
quartiles. The statistic ethnic HHI is calculated as the sum of the squared shares of each ethnicity in a city
and is somewhat lower for larger cities, indicating greater ethnic diversity.
3.2
Descriptive Evidence
Before testing the model’s predictions I first provide some descriptive evidence of how restaurant diversity
differs across cities. In Figure 4 the blue dots represent the number of cuisines (m1 left, m2 right) plotted
against the number of restaurants for all 726 Census Places, where both axes are in logs. As a point of
comparison, the red dots represent the average number of cuisines from 100 simulations in which for each
city I take r draws from a multinomial distribution that is uniform over all the cuisines, where r corresponds
18 I
dropped New Orleans because of damage from Hurricane Katrina, Anchorage, Alaska because the Census place geographic
definition is very different from other cities (it includes an enormous swath of virtually uninhabited land), and Industry, California,
which is almost entirely industrial (only 777 residents but many firms) and thus a very large outlier in restaurants per capita.
Washington, DC is not in my data set because the DC site was hosted by the Washington Post and used a completely different
page format, leading to difficulties in data collection.
19 It’s worth emphasizing that this is the “primary” cuisine for the restaurant; there may be German restaurants that serve
Austrian food and use “Austrian” as an additional cuisine but only one city has restaurants whose “primary” cuisine is Austrian.
12
Table 1: Summary Statistics
# Restaurants
# Cuisines (m1)
# Cuisines (m2)
Population 2007‐08 (thousands)
Land Area (sq km)
Density (Pop per sq km)
MSA Population 2000 (millions)
Average HH Size
Median HH Income (thousands)
Ethnic HHI
%Young (<35yrs)
%Old (>64yrs)
%College (completed for 25yrs+)
Mean
27.1
10.4
12.6
16.12
9.79
1,766
5.39
2.59
$50.0
0.79
14%
48%
33%
Land Qrt 4 (n=181)
Std. Dev.
[Min, Max]
29.4
[4, 192]
6.7
[2, 38]
11.0
[2, 78]
10.97
[3.14, 75.7]
3.16
[2.61, 14.93]
1,308
[326, 12143]
5.06
[0.30, 21.20]
0.45
[1.71, 4.37]
$17.6
[$17.7, $134.3]
0.19
[0.26, 0.99]
6%
[4%, 43%]
8%
[21%, 69%]
17%
[4%, 81%]
Mean
51.8
14.5
18.5
29.30
21.73
1,342
5.64
2.59
$50.9
0.80
13%
49%
36%
Land Qrt 3 (n=182)
Std. Dev.
[Min, Max]
51.9
[5, 359]
7.8
[3, 43]
13.6
[3, 96]
20.95
[4.6, 107.05]
4.28
[14.95, 29.99]
935
[243, 6429]
5.02
[0.30, 21.20]
0.32
[1.82, 3.59]
$16.6
[$24.2, $146.5]
0.19
[0.25, 0.99]
5%
[3%, 37%]
7%
[27%, 81%]
15%
[10%, 75%]
Mean
91.2
18.7
25.2
53.78
43.95
1,233
5.46
2.61
$56.2
0.78
12%
49%
39%
Land Qrt 2 (n=181)
Std. Dev.
[Min, Max]
72.0
[6, 380]
8.1
[3, 45]
14.5
[3, 90]
35.87
[6.11, 239.18]
9.10
[30.12, 61.31]
802
[175, 6191]
5.06
[0.15, 21.20]
0.29
[1.98, 3.65]
$19.3
[$26.8, $139.9]
0.18
[0.17, 1]
5%
[3%, 30%]
6%
[33%, 68%]
16%
[11%, 78%]
Mean
531.3
29.1
49.5
331.38
229.89
1,315
4.52
2.62
$49.1
0.76
10%
52%
36%
Land Qrt 1 (n=182)
Std. Dev.
[Min, Max]
1241.9
[8, 13664]
14.1
[3, 82]
40.7
[4, 277]
750.08
[7.15, 8328.5]
296.76 [61.54, 1962.37]
1,192
[55, 10601]
4.49
[0.15, 21.20]
0.31
[2.02, 4.12]
[$24.5, $111.8]
$15.4
0.15
[0.23, 0.97]
4%
[3%, 34%]
6%
[28%, 66%]
13%
[7%, 71%]
to the number of restaurants in that city20 . For the observed data in the cuisine measure 1 graph (left), as
the number of restaurants increases the number of cuisines first rises rapidly and then becomes roughly log
linear. The simulated data rises much more sharply in log linear form and then curves as the simulation hits
the maximum number of cuisines (90). The graph of cuisine measure 2 is quite similar except the observed
data appears to become log linear at an earlier point. What this comparison makes clear is that the number of
cuisines rises far more slowly with the number of restaurants than would be predicted from simply randomly
assigning cuisines to restaurants.
Not only is the number of cuisines across cities quite different from random assignment but there appears
to be a systematic relationship between the number of restaurants and the specific cuisines found in each city.
Following Mori, Nishikimi, and Smith (2008), who investigate empirical regularities in the distribution of
industries across cities, I show “Number Average Size” plots in Figure 5 for both cuisine measures. For
each cuisine I count the number of cities with that cuisine, “choice cities,” and calculate the average number
of restaurants found in those cities. In the figure on the left I plot the 90 cuisines with the choice cities on
the horizontal axis and the average number of restaurants on the vertical axis (blue dots); as an example,
the point (222, 462) corresponds to the Indian cuisine and indicates there are 222 cities with an Indian
restaurant and the average number of restaurants (across all cuisines) for those cities is 462. There is a
log-linear relationship with slope −1.6 between the average number of restaurants and choice cities such
that relatively rare cuisines (few choice cities) are found only in cities with large numbers of restaurants.
The small cluster of red dots around the point (300, 300) show the results from drawing from a multinomial
20 It
is sometimes suggested that I use the empirical distribution of restaurants across cuisines as a comparison distribution,
rather than the uniform multinomial. However, in this paper I wish to show features of the observed distribution and then suggest
a model that would generate this distribution. Further, there is no reason to assume that the observed distribution is exogenous,
and not in fact generated by features of cities. For example, we may believe that highly specialized doctors are found in large
cities because the pool of patients who might have a specific ailment is larger, or the supply of equipment and complementary
labor is greater, or a host of other features of large cities. If we took the empirical distribution of doctors to specialties and then
randomly assigned doctors to specialties from this distribution then of course large cities, which have more doctors, would have
more specialized doctors. However, this would not be a suitable test of the theory since the theory suggests a distribution and the
test would be effectively assuming that distribution.
13
#c
cuisines
20
40
# cuisines m
measure 2 (00's)
1
2
3 4
60 8
80100
Figure 4: Number of Cuisines vs Number of Restaurants
5
5
10 15
#Cuisines (m1)
# simulated cuisines
Results for 726 places, scale in logs
10 15
# restaurants (000's)
# restaurants (000's)
# cuisines measure 2 (00's)
(00 s)
# simulated cuisines measure 2 (00's)
(00 s)
Results for 726 places, scale in logs
(a) Cuisine Measure 1
(b) Cuisine Measure 2
distribution uniform over cuisines21 . While the simulated results also show a strong log-linear pattern all of
the cuisines are concentrated in a small range of choice city count and average number of restaurants. This
echoes the pattern of the earlier plots in that increasing the number of restaurants leads to far fewer new
cuisines than would be predicted by random assignment of cuisines to restaurants. In the figure on the right
I plot the 354 cuisines of measure 2 and also find a log-linear relationship (slope −1.1) but there is more
deviation for cuisines with few choice cities. Some of this likely stems from noise in the measure itself (see
earlier discussion) but it may also reflect the fact that by cutting the cuisines so finely (there are many found
in only one city) the average number of restaurants will have much more variance.
The plots in Figure 5 suggest a hierarchical relationship between cities and cuisines and so to test this
further I make use of the hierarchy test developed by Mori, Nishikimi, and Smith (hereafter “MNS”). Following MNS, I will define a hierarchical structure of cuisines across cities as a distribution such that a certain
cuisine will be found in a city only if all of the more common cuisines are also found in that city. In fact, a
quick look at the distribution of cuisines in Table 10 shows that certain types of restaurants (Chinese, Italian)
are found in most cities while other types (Afghan, Spanish) are found only in cities with a wide variety of
cuisines. In Figure 6 I show hierarchy diagrams for each cuisine measure. On the vertical axis I plot the
rank of cuisines by decreasing choice cities (rank 1 is the least common cuisine) and on the horizontal axis
I plot the rank of cities by increasing number of cuisines (the rank 1 city has the fewest cuisines)22 . Each
observation is a city-cuisine pair and it can immediately be seen that cities with more cuisines also have the
21 Specifically,
I randomly assign cuisines to every restaurant in every city, calculate the choice cities and average number of
restaurants for these cuisines, and then rank the cuisines by choice cities. I repeat this process 100 times and then take the average
across runs for cuisines of the same rank, and not across specific cuisine labels. To illustrate, the simulated average number of
choice cities for the rarest cuisine is the average of the rarest cuisine (fewest choice cities) in every run, whose label will differ
across runs.
22 While MNS plot the actual choice city count and number of industries I use the rank because there are cuisines with the same
count of cities, and cities with the same count of cuisines, and thus many observations would be hidden behind single points. Here
I break ties arbitrarily but use this only as a graphical method; in the formal testing of hierarchy I will follow the test from MNS
exactly, which allows for ties.
14
av
verage # re
estaurants (000's)
2
4
av
verage # restaurants ((000's)
5
6
8
1015
Figure 5: Number Average Size Plots: Average Number of Restaurants in Cities with a Given Cuisine
200
400 600800
200
# choice cities
average
g # restaurants
average
g # restaurants ((simulated data))
Results for 726 places, scale in logs
400 600800
# choice cities
average
g # restaurants
average
g # restaurants ((simulated data))
Results for 726 places with cuisine measure 2, scale in logs
(a) Cuisine Measure 1
(b) Cuisine Measure 2
rarer cuisines.
The basic structure of the MNS hierarchy test is to take as given the number of cuisines in each city (as
found in the data) and then test the null hypothesis that cuisines are randomly assigned. In some ways this
serves as a test for the asymmetry of types: if I cannot reject that all cuisines are equally likely to be assigned
to a city then there is no point in focusing on the composition of variety. Consider the matrix of cuisine-city
indicators, with cuisines sorted by ascending city choice count and cities by ascending numbers of cuisines,
as seen in the plots in Figure 6. For each cuisine-city pair, MNS define a hierarchy event as a binary variable
equal to one only when all cities with greater or equal number of cuisines also have that cuisine. Graphically,
for each dot a hierarchy event occurs if all other slots in the same row to the right of the dot are filled. As
an example, if 725 of the cities have cuisine v and the city missing cuisine v has the fewest overall number
of cuisines (furthest to the left) then a hierarchy event occurs for all cuisine-city pairs in cuisine v’s row.
However, if instead the city missing the cuisine was the city with the most overall cuisines (furthest to the
right), then there would not be a hierarchy event for any of the cuisine-city pairs. It’s important to note that
if two cities have the same number of overall cuisines but one of the cities is missing cuisine v then neither
city has a hierarchy event for cuisine v. MNS define the hierarchy share as the percentage of cuisine-city
pairs that are hierarchy events, or graphically, the percentage of dots that are hierarchy events.
Having defined the hierarchy share, I then test the null hypothesis that cuisines are randomly assigned
to cities, with the number of cuisines in each city fixed and equal to the observed count. In other words,
a city with just one type of cuisine should be no more likely to have a Chinese restaurant than an Afghan
restaurant. Rather than deriving the distribution of the hierarchy-share statistic, I will run a simulation to
estimate the cumulative distribution function of hierarchy share and then accept or reject the null hypothesis
of no hierarchy. The procedure is for each city m draw #vm varieties from the total set V and then calculate
the hierarchy-share. I repeat this procedure 10, 000 times to get a distribution of hierarchy-share under the
null hypothesis23 .
23 Another
possible reference distribution would be that generated by drawing restaurants from a multinomial distribution uniform over cuisines, rather than drawing cuisines, as was done for comparison with the log cuisines against log restaurants graphs
15
cuisine rank (ascending b
by count off choice citties)
0
100
200
3
300
400
cuisine rank (ascending b
by count off choice citties)
0
20
40
60
80
100
Figure 6: Hierarchy Diagrams
0
200
400
600
city rank (ascending by count of cuisines)
Data for 726 places, cuisine measure 1
800
0
200
400
600
city rank (ascending by count of cuisines)
800
Data for 726 places, cuisine measure 2
(a) Cuisine Measure 1
(b) Cuisine Measure 2
When I calculate the hierarchy share for all 726 places I find a hierarchy share of 23% for cuisine
measure 1 and 15% for cuisine measure 2, with both statistics highly significant (the largest values from
10000 simulated runs were 2.9% and 3.6% for cuisine measures 1 and 2, respectively). For comparison,
MNS found that the distribution of industries in Japan in 1999 had a hierarchy share of 71%, much larger
than the shares I find here. Nonetheless, the hierarchical structure of cuisines across cities is still very
far from random and is rather surprising considering that cities differ dramatically in ethnic composition,
income, family size, education, and other factors that may affect the cuisines offered.
To show how this hierarchy relates to popuation and land area I estimate a very simple version of my
model with linear thresholds and no demographic characteristics. Let Cmv be a binary variable indicating
whether variety v exists in market m with a population threshold that is linear in land area:
{
∗
1 if Nm − αv ∗ Lm ≥ Nδv
(19)
Cmv =
0 o/w
A restaurant of cuisine v only locates in market m if the population, Nm , is above a threshold that increases
with cuisine-specific slope αv in land area Lm . If I allow for some unobserved heterogeneity in tastes then I
can rewrite the above equation with error term εmv and estimate as a limited dependent variable model:
Pr(Cmv = 1) = Pr(Π∗mv > 0)
Π∗mv = γ1v Nm + γ2v Lm + ηv + εmv
Following the theory, I expect the γ1 ’s to be positive, the γ2 ’s to be negative, and the cuisine fixed effects,
2v
represents the αv parameter24 , which gives the number of additional
ηv ’s, to be negative. Further the ratio γγ1v
in Figure 4. The problem with this procedure is that many cities then receive most or all cuisines, whereas not a single city in
the data has all the cuisines, thus greatly increasing the number of cuisine-city pairs from that observed. However, this reference
distribution was tested in Figure 4 in a fairly similar exercise and clearly does not generate the observed hierarchical structure.
24 In the model a cuisine is found in a city if the population is greater than the threshold frontier for a given land value. This
requires the coefficient on population be equal to one, which is equivalent to dividing the estimation results by γ1v (coefficient on
population).
16
people required for a city to have a cuisine, along the frontier, if the land area is increased by one unit. The
∗
ratio γη1vv gives the population intercept for each cuisine ( Nδv )—the minimum number of people if there was
no land/transportation cost. Both ratios should be greater for rarer cuisines. I assume that the error term is
distributed standard logistic and estimate the above specification with a logit model25 . I estimate each cuisine
separately and exclude cuisines when the estimated model fails a likelihood ratio test at the 5% level26 . I
restrict the analysis to cuisine measure 1, which has no missing data and thus yields a clearer interpretation.
Overall, I find that 82 of the 85 cuisines have a positive population intercept of which 74 are significant
at the 10% level and 68 at the 5% level27 . In the left panel of Figure 7 I plot all the positive population
intercepts significant at the 10% level against the corresponding city count with log axes. The clear log-linear
relationship shows that the fewer the number of cities with a cuisine, the larger the population intercept28 .
Turning to the frontier slope estimates (αt ’s) I find that 60 of the 85 estimates are positive with 36 significant
at the 10% level and 34 significant at the 5% level. The right panel of Figure 7 shows the positive and
significant (10% level) slope estimates against city count and again a strong log-linear pattern emerges.
This is consistent with the model’s prediction that rarer cuisines are only found in bigger, denser cities and
suggests a fairly consistent ordering of tastes across cities, even if the actual proportions differ.
es
stimated slope on sq km land arrea (000's)
1
2
3
4
estimated p
e
population threshold (millions)
5
10 15
Figure 7: Plotting intercept and slope threshold estimates against city count
200
200
400 600
Results for 74 cuisines with population thresholds significant at 10% level, scale in logs
400 600800
# choice cities
# choice
h i cities
iti
Results for 36 cuisines with slope estimates significant at 10% level, scale in logs
(a) Intercept estimates
(b) Slope estimates
These results suggest certain parallels to the central place theory of Christaller (Christaller and Baskin
1966) and Lösch (Lösch 1967) which posits a hierarchical structure of cities with larger cities offering goods
and services not provided by smaller cities. In fact, a recent paper by (Hsu 2011) offers a model of central
25 I
also estimated the model with a probit and found similar results but with a slightly lower log likelihood for most cuisines.
model failed the likelihood ratio test for some of the cuisines found in very few cities, specifically: “Burmese” (4 cities),
“Dim Sum” (4), “Polish & Czech” (4), “Tibetan” (3), and “Chowder” (6).
27 I used the ”nlcom” package of Stata which uses the delta method to compute standard errors for the ratio of coefficients.
28 I restricted the plot to positive estimates in order to show the strong log-linear relationship however it is informative to look
at the three cuisines that had negative population intercept estimates: “Deli,” “Fast Food,” and “Pizza.” These three cuisines are
found in nearly every city and are thus consistent with the general downward sloping pattern between population and city count.
Additionally, they may benefit the least from locating in a large dense market since they represent fairly common tastes and are
found in many locations in large markets, often with multiple outlets of the same franchise.
26 The
17
place theory using scale economies in production but also notes that heterogeneity in demand would lead
to the same hierarchical structure of goods across cities. This heterogeneity in demand is consistent with
my model–in some sense I am focusing on the role of population characteristics and space in generating
the heterogeneity across cities–and thus these results may also provide evidence in support of central place
theory.
4
Empirics
4.1
City level estimation
As outlined in the theory section, without substantial similarities in tastes and demographics across markets
I cannot make robust predictions about the count of varieties. However, the strong hierarchical results
presented in the previous section suggest a fair amount of similarity in tastes across my sample cities. To
look at this more closely I run regression specifications exploring the relationship between variety count,
population, and land area while controlling for demographic characteristics. The model suggests that under
the assumption of equal variety-specific affinities across groups, (βsv = βv ), the ranking of cuisine counts
across cities follows:
) [(
(
)
]
S
Lm
L∗
Nms
∗
∗
1 − ∗ 1(Lm ≤ L ) +
1(L < Lm )
(20)
#Varietiesm ∼ Nm ∑
2L
2Lm
s=1 Nm
I approximate this specification by taking logs and replacing the log of the percentage sub-groups ( NNms
)
m
with the vector Xm of demographic percentages and population characteristics (ex: median income, percent
college educated) shown in Table 1. With summary level data I cannot separate individuals into mutually
exclusive groups, as implied by the model, and so I let each characteristic have its own coefficient. After
taking logs and simplifying there are two terms with land area: ln(2L∗ − Lm )1(Lm ≤ L∗ ) and −ln(Lm )1(L∗ <
Lm ). The form of the first term is dependent upon functional form assumptions from the model, such as linear
transporation cost. However, the prediction of a negative effect of log land area, and one that increases in
magnitude with larger values of land, is a more general finding and would also hold, for example, under an
assumption of quadratic transportation costs. To capture this I replace the complicated kinked function with
the log of land area, ln(Lm ), and estimate regressions by land quartile to allow the coefficients to vary with
land area29 . These simplifications lead to a straight-forward log linear specification:
ln(#Cuisinesm ) = γ0 + γ1 ln(Nm ) + γ2 ln(Lm ) + Xm ′β + εm
(21)
In equation 21 the m subscripts stand for market (city), N is population with γ1 predicted to be positive, L
is land with γ2 predicted to be negative, and X is the vector of covariates shown in summary Table 1. The
coefficients on demographic characteristics are not cuisine specific and in the context of the theory could
be interpreted as averages of the affinities across cuisines. In Table 2 I run this specification separately
by land quartile, pooled, and for both cuisine measures. I include MSA fixed effects for all the quartile
specifications, which reduces the sample by 23 cities; running the quartile specifications without fixed effects
leads to very similar coefficients and smaller standard errors. The first two columns of each panel of Table
2 compare the pooled specifications with and without MSA fixed effects, yielding little difference. In the
pooled specifications I find that a 10% increase in population leads to a 4% increase in the count of cuisines
kink point L∗ is a general feature of this model under different assumptions. I discuss the difficulties of estimating this
parameter later in the paper.
29 The
18
Table 2: Number of Cuisines
Log # Cuisines Measure 1
All
All
Land Qrt4 Land Qrt3 Land Qrt2 Land Qrt1
Pop 2007‐8 (logs)
0.410*** 0.410*** 0.332*** 0.397*** 0.446*** 0.457***
[0.026]
[0.029]
[0.090]
[0.074]
[0.050]
[0.059]
Land sq mtrs (logs)
0.007
0.012
0.200*
0.076
0.045
‐0.149**
[0.024]
[0.030]
[0.108]
[0.144]
[0.117]
[0.063]
Average HH Size
‐0.442*** ‐0.479*** ‐0.513*** ‐0.456*** ‐0.301** ‐0.393
[0.068]
[0.080]
[0.151]
[0.159]
[0.132]
[0.237]
Median HH income (000's)
0.004**
0.003
0.002
0.004
‐0.003
‐0.002
[0.002]
[0.002]
[0.005]
[0.003]
[0.005]
[0.005]
Ethnic HHI
‐0.715*** ‐0.543*** ‐0.888** ‐0.812*** ‐0.462*
0.082
[0.100]
[0.131]
[0.346]
[0.213]
[0.242]
[0.242]
0.293
0.292
0.989
1.307
‐1.060
‐0.086
%Old (>64)
[0.518]
[0.562]
[1.462]
[1.131]
[1.207]
[1.431]
%Young (<35)
0.095
‐0.161
0.774
0.223
‐1.277
‐0.296
[0.415]
[0.426]
[1.293]
[0.725]
[1.029]
[0.918]
%College grad
0.593*** 0.619***
0.734
0.661*
0.983** 0.917**
[0.158]
[0.176]
[0.443]
[0.370]
[0.415]
[0.401]
MSA Fixed Effects
NO
Yes
Yes
Yes
Yes
Yes
Constant
‐0.520
‐0.757
‐2.607
‐1.428
‐0.849
1.241
[0.428]
[0.524]
[1.754]
[2.449]
[2.147]
[1.110]
Observations
726
703
177
172
175
179
R‐squared
0.791
0.836
0.697
0.836
0.856
0.910
Robust standard errors in brackets, *** p<0.01, ** p<0.05, * p<0.1
Note: 23 Census Places in sample are not in MSAs and were dropped from fixed effect estimation
All
0.513***
[0.027]
0.024
[0.026]
‐0.647***
[0.082]
0.007***
[0.002]
‐0.975***
[0.118]
‐0.191
[0.604]
0.161
[0.485]
0.364**
[0.176]
NO
‐1.018**
[0.485]
726
0.825
Log # Cuisines Measure 2
All
Land Qrt4
Land Qrt3
0.512*** 0.471***
0.459***
[0.030]
[0.094]
[0.080]
0.020
0.204*
0.071
[0.031]
[0.114]
[0.152]
‐0.670*** ‐0.647***
‐0.730***
[0.091]
[0.161]
[0.167]
0.004*
0.005
0.006*
[0.002]
[0.005]
[0.004]
‐0.747*** ‐0.897**
‐0.956***
[0.151]
[0.388]
[0.222]
0.200
0.724
0.604
[0.610]
[1.520]
[1.252]
‐0.199
0.657
‐0.131
[0.477]
[1.371]
[0.874]
0.537***
0.565
0.502
[0.195]
[0.450]
[0.401]
Yes
Yes
Yes
‐1.087*
‐3.403*
‐0.751
[0.593]
[1.827]
[2.646]
703
177
172
0.872
0.735
0.864
Land Qrt2 Land Qrt1
0.532*** 0.566***
[0.062]
[0.054]
0.025
‐0.088
[0.166]
[0.063]
‐0.580*** ‐0.445*
[0.175]
[0.243]
0.001
‐0.005
[0.007]
[0.005]
‐0.714**
‐0.109
[0.318]
[0.265]
‐1.355
‐0.955
[1.551]
[1.694]
‐0.888
‐1.649
[1.269]
[1.179]
0.960*
1.168**
[0.547]
[0.448]
Yes
Yes
‐0.473
0.243
[2.899]
[1.380]
175
179
0.852
0.929
(measure 1) and a 5% increase in the count of cuisine-price pairs (measure 2). I also find that more ethnically
diversity cities (lower ethnic HHI), cities with a larger percentage of college graduates, and cities with a
lower average household size have a greater number of cuisines (perhaps reflecting economies of scale in
food preparation or disutility from taking young children to restaurants). The coefficient on land area is
insignificant for both pooled specifications. In the land quartile specifications I find that the effect of ethnic
diversity and average household size declines monotonically as land area increases moving from quartile
1 to 4 while the effect of population grows in magnitude. Further, the coefficient on land area declines
over the quartiles until reaching the last quartile where it becomes negative and statistically significant for
cuisine measure 1 (although not for the noisier cuisine measure 2). The magnitude of this coefficient is fairly
large, indicating that a 10% decrease in land area, which effectively increases density without changing
population, increases the number of cuisines by 1.5%. These results, at best, seem to offer weak evidence
that land area has any effect on variety but given that the model makes no robust predictions on variety count
across markets I now turn to estimation at the variety (cuisine) level.
4.2
Cuisine level estimation
The theory suggests that for any variety, regardless of tastes, markets with greater populations and smaller
land areas aggregate consumers and are thus more likely to support that variety. Continuing with Cmv as an
indicator I write:
)
(
⎧
[(
]
S
)

N
ms
Lm
⎨1 if N
L∗
∗
∗
1 − 2L∗ 1(Lm ≤ L ) + 2Lm 1(L < Lm ) ≥ N ∗
m ∑ βsv
N
(22)
Cmv =
m
s=1

⎩
0 o/w
An interesting feature of the model is that the kink point L∗ is independent of the variety and the demographic characteristics of the population. This kink point exists because until the firm can reach the desired
geographic market extent, the density adjusts with the land area in a way dependent upon transportation cost.
When the market’s land area is larger than L∗ the firm is able to operate at its preferred geographic extent
19
(L∗ /2 on either side) and thus only needs the market to be above a constant density so that it can always sell
to the same number of consumers within this distance. In this way the kink point is a very general feature
of these models and implies that different assumptions about transportation cost will still lead to land area
having a larger negative effect for geographically bigger markets30 . For this reason it would be informative
to estimate the kink point directly and let the coefficient on ln(Lm ) vary depending on whether Lm ≤ L∗ ,
making L∗ an unknown structural break. However, the data is too sparse in that many geographically small
markets lack many cuisines, and thus a cut-off value in land area perfectly predicts the absence of that
cuisine. Therefore I once again run my estimates with just one term for land area.
As before, I take the log of equation 22 and replace the sub-group percentages with population characteristics. The 2000 US Census lists population by country of birth for every Census place and I add the
percentage of the population whose ethnicity matches the corresponding cuisine to the list of covariates. I
then estimate the probability of each market having each cuisine:
Pr(Cmv = 1) = Pr(Π∗mv > 0)
Π∗mv = γ1 ln(Nm ) + γ2 ln(Lm ) + Xm ′β + ηv + εmv
I first estimate a pooled specification of the above across all cuisines, breaking out results by land quartile,
and including cuisine fixed effects, a constant, and clustering standard errors at the city (place) level. The
number of observations will be greater for larger land quartiles since cities in these quartiles have a greater
number of cuisines. The estimates in Table 3 show that across all cuisines the likelihood of a city having
a given cuisine is increasing in population and decreasing in land area. Looking at the estimates by land
quartile, we again see that most of the effect of land comes from the largest cities. The second column under
each sub-heading includes ethnicity and decreases the samples since non-ethnic cuisines (e.g., “Desserts”)
have no corresponding ethnicity. Increasing the percentage of the population of a given ethnicity significantly
raises the likelihood of that city having the corresponding cuisine but doesn’t much change the effects of the
other factors.
I now estimate the above specification for each cuisine separately, including all the previous covariates
except for the age variables, which I found to be insignificant. Again, I throw out the results for cuisines
not passing the likelihood ratio test, leaving 86 of the 90 cuisines. The estimation results are listed in the
Appendix in Table 9. Generally the coefficients reflect the signs from the pooled specification in Table
3 but with larger standard errors (the sample size is much smaller). All of the coefficients on population
are positive and significant at the 5% level. The coefficient on land is negative for 65 of the 86 cuisines
with 27 of these significant at the 10% level. The variable “average household size” tends to decrease the
likelihood of having a cuisine while percent college educated and percent of the corresponding ethnicity
raise the likelihood. In Table 4 I show classification results for the full model versus a logit model with
just a constant. There are 86 cuisines and 726 cities resulting in 62, 436 cuisine-city pairs. The rows of the
table show the actual count of cities with a cuisine (1 if yes) while the columns show the predictions of the
constant-only model and the full model. We can see that because most observations are zero, meaning most
cities are missing most cuisines, the overall classification rate is high for both models: 86.4% for the model
with just a constant and 91.5% for the full model. However, there is a large difference in the number of
correctly predicted successes, meaning the full model does a much better job in correctly predicting whether
a city has a cuisine (76% to 59%).
(
S
Nms
∑ βsv Nm
s=1
)
[(
)
]
2
Lm
3L∗
∗
∗
∗
the quadratic case variety v is found in market m if Nm
1 − 3L
∗2 1(Lm ≤ L ) + 2Lm 1(L < Lm ) ≥ N ,
√
4
where L∗ = 3τ
(u1 − u0 − c) and N ∗ , which by definition does not depend upon transportation cost, is the same (N ∗ = u1 −uF0 −c ).
30 In
20
Table 3: Likelihood of having a given cuisine
Coefficients (marginal effects)
Pop 2007‐8 (logs)
Land sq mtrs (logs)
Average HH Size
Median HH income (000's)
%Old (>64)
%Young (<35)
%College grad
%Corresponding Ethnicity
Cuisine Fixed Effects
Observations
Number of cuisines
Pseudo R‐squared
Clustered standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1
All
Cuisine Cuisine Indicator Indicator
0.1005*** 0.0816***
[0.0032]
[0.0026]
‐0.0192*** ‐0.0212***
[0.0034]
[0.0028]
‐0.0569*** ‐0.0396***
[0.0108]
[0.0088]
0.00
0.00
[0.0003]
[0.0002]
‐0.0524
0.0168
[0.0911]
[0.0721]
‐0.0707
‐0.0377
[0.0725]
[0.0551]
0.1642*** 0.1653***
[0.026]
[0.0213]
0.1919***
[0.0198]
YES
YES
65340
42834
90
59
0.59
0.62
(726 clusters)
Land Qrt4
Land Qrt3
Cuisine Cuisine Cuisine Cuisine Indicator Indicator Indicator
Indicator
0.0873*** 0.0838*** 0.1134*** 0.1010***
[0.0099]
[0.0094]
[0.0083]
[0.0067]
0.0223
0.0158
‐0.0113
‐0.0306
[0.0126]
[0.013]
[0.026]
[0.0211]
‐0.0548** ‐0.0470* ‐0.0419*
‐0.0294
[0.021]
[0.0197]
[0.0213]
[0.0166]
0.00
0.00
0.00
0.00
[0.0006]
[0.0005]
[0.0006]
[0.0005]
0.0334
0.0283
0.0469
0.0636
[0.1789]
[0.1452]
[0.188]
[0.1583]
0.0842
0.0483
‐0.1781
‐0.1088
[0.1768]
[0.1419]
[0.1372]
[0.1085]
0.2075*** 0.1886*** 0.1784*** 0.1742***
[0.0523]
[0.0526]
[0.0538]
[0.0451]
0.2053***
0.2337***
[0.0464]
[0.0447]
YES
YES
YES
YES
11946
6697
12558
7462
66
37
69
41
0.45
0.48
0.52
0.55
(181 clusters)
(182 clusters)
Land Qrt2
Cuisine Cuisine Indicator
Indicator
0.1400*** 0.1228***
[0.0083]
[0.0084]
‐0.0177
‐0.0127
[0.0227]
[0.0229]
‐0.0750**
‐0.0591*
[0.0258]
[0.0265]
0.00
0.00
[0.0007]
[0.0007]
‐0.0184
0.1351
[0.2181]
[0.21]
‐0.049
0.0395
[0.1867]
[0.1735]
0.2508*** 0.2682***
[0.0641]
[0.0633]
0.2328***
[0.0436]
YES
YES
12670
7240
70
40
0.55
0.58
(181 clusters)
Table 4: Full Model Classification Table
Predicted
0
Actual
1
Cons Only
Full
Cons Only
Full
0
46,136
47,095
5,410
3,161
21
94%
96%
41%
24%
1
3,103
2,144
7,787
10,036
6%
4%
59%
76%
Total
49,239
49,239
13,197
13,197
Land Qrt1
Cuisine Cuisine Indicator
Indicator
0.1395*** 0.1221***
[0.0058]
[0.0052]
‐0.0445*** ‐0.0383***
[0.0071]
[0.0065]
‐0.0969** ‐0.0770**
[0.0333]
[0.0294]
0.00
0.00
[0.0008]
[0.0007]
‐0.3273
‐0.0206
[0.2838]
[0.2637]
‐0.1284
‐0.0236
[0.177]
[0.1711]
0.2528*** 0.2766***
[0.0731]
[0.0664]
0.3941***
[0.0825]
YES
YES
16380
10738
90
59
0.63
0.65
(182 clusters)
In order to better interpret the results of the estimation I now do a counterfactual exercise to see the
aggregate effect–across all cuisines–of individual city characteristics on product variety. I will focus on the
main demand aggregation variables–population, land, and ethnicity–and use percent college educated for
comparison31 . I first use the model to predict whether each of the 726 cities has each of the 86 cuisines.
Next I calculate the standard deviation of each explanatory variable over all cities, calculating standard
deviation separately for each ethnicity32 . For each explanatory variable I again predict all city-cuisine pairs
after increasing the variable by one standard deviation, or in the case of log land, decreasing by a standard
deviation.
The results, shown in aggregate in Table 5 and by cuisine in Table 6, yield a fairly clear interpretation.
Population is the most important factor in determining city product variety but the effects vary greatly by
land quartile. For the quartile 4 cities, a one standard deviation increase in city population increases the
average count of cuisines by 145% while the same increase leads to 57% more cuisines for quartile 1 cities.
Further, for smaller cities over half of this increase comes from new non-ethnic cuisines while in the top two
quartiles the increase is larger in ethnic cuisines. A one standard deviation decrease in log land area, which
increases density without changing the population, has a fairly large effect at the top quartile comparable to
increasing the percent of the population with a college education by one standard deviation. The size of this
effect decreases with each land quartile and nearly drops to zero for quartile 4. Table 6 shows that for some
cuisines, including both “American” cuisines, “Barbecue,” “Coffee Shops & Diners,” “Desserts,” “Mexican,”
“Seafood,” and “Steakhouse”–decreasing land area leads to fewer cities having this type of food. These are
some of the most common cuisines and thus make up a significant portion of the variety of small cities.
Mechanically, since the estimation predicts that decreasing land decreases the likelihood of having these
cuisines, small cities can end up with fewer cuisines overall. Many of these small cities have a population
below the minimum population required for many cuisines, given the cities’ demographic characteristics,
and thus decreasing land area should not increase their likelihood of having those cuisines. To be clear, this
suggests land area should have no effect, not a negative effect, and there is nothing in the model that would
predict a decrease in land area leads to a decrease in the likelihood of having a cuisine. However, these
are relatively few cuisines in comparison to the majority and the general effect is negative, as seen in the
coefficient on land area found in Table 3.
Finally, increasing the percentage of the population from each ethnicity has a positive and significant
effect on the count of ethnic cuisines in a city. As with population, this effect is largest, in percent terms, for
the smallest cities. Taken all together Table 5 suggests that for small cities, product variety is low mainly due
to population size, with low ethnic diversity leading to few ethnic cuisines. Increasing population density,
while maintaining population size, does not lead to greater product variety because these small cities just
don’t have enough people at any geographic aggregation. As cities get larger population alone become less
important and the distribution of people in space begins to affect which varieties are available; a city may
have sufficient demand for a given cuisine but that demand must be concentrated.
31 Decreasing
average household size by one standard deviation also had a significant effect, slightly larger than the effect for
percent college educated. To save space these results are omitted but results for all variables are available by request.
32 I use standard deviation, rather than a uniform percentage change, because I am interested in the magnitude of the effect of
each variable within the range of variation actually observed across cities. If I were to increase each variable by 10% this would
represent a fairly tiny change in population given the variance across cities but an absolutely enormous change in the percentage of
the population of a given ethnicity; for most ethnicities it would increase the ethnic percentage far beyond the maximum observed
value in my data. Finally, note that increasing or decreasing a variable in logs by a fixed amount is equivalent to applying a
percentage change to the variable.
22
Table 5: Predicted Change in Cuisine Count
ΔPopulation
ΔLand
ΔCollege
ΔEthnic
Land Quartile Cuisine Type Baseline Count Change in cuisine count Change in cuisine count Change in cuisine count Change in cuisine count
Non‐ethnic
15.60
6.03
39%
0.91
6%
1.10
7%
0.00
0%
1
Ethnic
12.69
10.18
80%
1.84
15%
1.77
14%
1.67
13%
Total
28.30
16.20
57%
2.75
10%
2.87
10%
1.67
6%
Non‐ethnic
10.82
6.04
56%
0.56
5%
0.70
6%
0.00
0%
2
Ethnic
7.18
7.05
98%
0.75
10%
0.99
14%
1.56
22%
Total
18.01
13.09
73%
1.31
7%
1.69
9%
1.56
9%
Non‐ethnic
7.41
6.48
87%
0.06
1%
0.62
8%
0.00
0%
3
Ethnic
5.34
5.41
101%
0.35
7%
0.72
13%
1.25
23%
Total
12.75
11.90
93%
0.41
3%
1.34
10%
1.25
10%
Non‐ethnic
4.49
6.93
154%
0.22
5%
0.57
13%
0.00
0%
4
Ethnic
3.52
4.68
133%
0.00
0%
0.59
17%
1.24
35%
Total
8.01
11.61
145%
0.22
3%
1.16
14%
1.24
15%
*Table shows average change in count of cuisines resulting from a one standard deviation decrease in log land area and a one standard deviation increase in every other variable. Percent change is calculated as percent of baseline count.
4.3
Identification issues and clustering of ethnic populations
Estimating the effect of population concentration on product variety shares identification issues with the
problem of estimating the effect of population concentration on wages and much of the following discussion
is informed by Combes, Duranton, and Gobillon (2011), or CDG. One potential concern is that restaurant
diversity, or another factor correlated with restaurant diversity, actually increases population concentration
(the “endogenous quantity of labor” problem in CDG). While this reverse channel must be present to some
extent, and is in fact a motivation for studying city consumption amenities, it is likely a much smaller problem
than in the agglomeration productivity literature since restaurant diversity and correlated factors may have
less influence on city location decisions than wages. In Glaeser and Gottlieb (2009) the authors argue that the
existence of a real wage premium in large cities provides evidence that consumer amenities are not the main
driver of urban concentration in the United States. Perhaps a more worrisome problem is if particular groups
of people associated with restaurant diversity sort into large, dense cities (this is somewhat similar to the
“endogenous quality of labor” problem in CDG). For example, if producers of cuisine v tend to live in large,
dense cities for reasons unrelated to demand for cuisine v—new immigrants may be skilled restaurateurs and
feel more comfortable in large cities—then this would generate a spurious relationship between population,
land, and product variety. Another example would be if people with a particularly strong taste for variety–
gourmands–prefer to live in big cities and thus the restaurant variety is being driven by a small subset of the
population.
Ideally, with a dataset on restaurateurs I could compare similar producers of cuisine v in different cities,
or the same restaurateur living in different cities over time, and show that a producer of cuisine v only creates
a restaurant of cuisine v when demand in their current city is sufficiently aggregated. Since I don’t have this
data, I will proxy for the presence of both producers and consumers of cuisine v with the population of
ethnicity v and show that even after controlling for the size of this population, the spatial concentration of
the population increases the likelihood of having a restaurant of cuisine v. Following the model, if population
subgroups with an affinity for a particular variety are clustered in space, rather than uniformly distributed
as assumed earlier, then this clustering would lower the minimum population required for entry of that
variety. While spatial concentration of a particular population would also be consistent with a supply-side
23
Table 6: Predicted Change in City Count, by Cuisine
Cuisine
Afghan
African
American (New)
American (Traditional)
Argentinean
Armenian
Asian
Austrian
Bakeries
Barbecue
Belgian
Brazilian
Burmese
Cajun & Creole
Californian
Cambodian
Caribbean
Central European
Chilean
Chinese
Coffee Shops & Diners
Colombian
Cuban
Deli
Desserts
Dim Sum
Eastern European
Eclectic & International
Egyptian
English
Ethiopian
Filipino
French
German
Greek
Hamburgers
Health Food
Hot Dogs
Hungarian
Indian
Indonesian
Irish
Italian
Jamaican
Japanese
Korean
Kosher
Lebanese
Malaysian
Mediterranean
Meat‐and‐Three
Mexican
Middle Eastern
Moroccan
Noodle Shop
Latin American
Pizza
Polish & Czech
Polynesian
Portuguese
Puerto Rican
Russian
Scandinavian
Seafood
Soups
South American
Southern & Soul
Southwestern
Spanish
Steakhouse
Sushi
Swiss
Tapas / Small Plates
Thai
Tibetan
Turkish
Vegan
Vegetarian
Venezuelan
Vietnamese
Fast Food
Coffeehouse
Pan‐Asian & Pacific Rim
Family Fare
Cheesesteak
Chowder
Ice Cream
Bagels
Donuts
Juices & Smoothies
ΔPopulation ΔLand ΔCollege ΔEthnic Original Count of Cities
Change in city count
Change in city count
Change in city count
Change in city count
LQ4 LQ3 LQ2 LQ1 Sum LQ4 LQ3 LQ2 LQ1 Sum LQ4 LQ3 LQ2 LQ1 Sum LQ4 LQ3 LQ2 LQ1 Sum LQ4 LQ3 LQ2 LQ1 Sum
2
2
4
9
17
4
4
7
27
42
1
3
1
6
11
0
2
0
2
4
0
2
0
0
2
1
2
4
20
27
3
4
5
50
62
0
1
0
8
9
0
1
0
17
18
0
0
0
1
1
21
45
68 119 253
36
79 100
39 254
0
‐2
0
‐1
‐3
3
8
10
7
28
‐1
‐3
‐1
‐2
‐7
91 128 153 173 545
89
36
6
3 134
‐16 ‐12
‐4
‐1 ‐33
‐8
‐6
‐3
0 ‐17
‐3
‐3
‐1
0
‐7
1
1
1
10
13
2
3
0
21
26
0
1
0
3
4
1
1
0
3
5
0
0
0
0
0
Not Estimated
41
63
90 128 322
83
96
83
29 291
5
6
15
6
32
‐1 ‐15 ‐14 ‐13 ‐43
14
13
25
11
63
Not Estimated
57
83 112 152 404 121
77
44
17 259
18
13
18
5
54
5
4
8
1
18
0
0
0
0
0
65 121 151 170 507
89
35
2
0 126
‐38 ‐74 ‐19
‐2 ‐133
58
30
2
0
90
0
0
0
0
0
0
0
0
7
7
1
2
4
30
37
0
0
0
‐4
‐4
0
0
0
‐5
‐5
0
0
0
5
5
4
1
8
21
34
4
4
20
60
88
0
1
0
9
10
1
2
1
16
20
0
1
0
5
6
0
1
1
2
4
0
2
0
2
4
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
6
31
30
81 148
13
45
81
79 218
0
0
9
10
19
0
2
21
24
47
0
0
0
0
0
13
19
32
70 134
21
36
78
75 210
2
4
11
8
25
2
4
12
8
26
0
0
0
0
0
0
1
0
4
5
5
5
3
29
42
2
3
1
10
16
1
0
0
6
7
0
0
0
1
1
6
14
17
59
96
8
12
33
57 110
0
1
1
2
4
0
2
1
6
9
1
2
2
9
14
0
0
2
5
7
5
4
7
20
36
0
0
0
0
0
0
0
‐1
0
‐1
0
1
2
0
3
0
0
0
3
3
0
0
0
8
8
0
0
0
‐1
‐1
0
0
1
10
11
0
0
0
1
1
148 169 175 178 670
12
1
0
0
13
1
0
0
0
1
4
1
0
0
5
11
1
0
0
12
42
72 106 153 373
95 103
47
14 259
‐7 ‐17 ‐22
‐2 ‐48
2
3
10
6
21
0
0
0
0
0
0
0
1
9
10
1
3
2
28
34
0
0
0
5
5
0
0
0
3
3
0
0
0
0
0
4
2
7
30
43
13
19
41
82 155
2
3
4
26
35
1
0
0
4
5
1
1
2
10
14
119 147 163 171 600
35
13
3
2
53
0
0
0
0
0
6
1
0
0
7
0
0
0
0
0
76 107 137 162 482 118
60
13
3 194
‐8
‐9
‐3
‐2 ‐22
‐7
‐9
‐3
‐2 ‐21
0
0
0
0
0
1
0
1
2
4
0
2
0
2
4
0
0
0
1
1
0
2
0
1
3
0
0
0
0
0
4
4
0
13
21
6
6
8
48
68
3
4
1
15
23
0
2
0
0
2
0
1
0
0
1
14
21
40
80 155
23
49
87
75 234
2
2
12
16
32
1
2
10
11
24
0
0
0
0
0
Not Estimated
3
5
5
24
37
9
10
27
67 113
0
1
1
17
19
‐1
0
‐1
‐4
‐6
0
1
0
2
3
2
1
0
11
14
4
3
3
33
43
0
1
0
8
9
0
1
0
10
11
0
0
0
1
1
1
1
1
6
9
4
2
11
26
43
1
0
1
5
7
0
‐1
0
‐2
‐3
1
0
0
1
2
32
52
77 111 272
38
70
82
43 233
1
3
6
2
12
12
33
46
29 120
3
11
23
13
50
4
6
17
58
85
2
3
23
53
81
0
0
0
2
2
0
0
0
‐5
‐5
0
0
3
4
7
17
43
53 114 227
45
75
95
55 270
3
5
10
7
25
3
9
17
16
45
3
9
17
16
45
30
51
73 126 280
79
97
86
36 298
4
14
23
14
55
0
2
2
0
4
0
0
0
0
0
3
5
6
54
68
1
3
11
42
57
0
0
‐1
‐2
‐3
0
3
2
21
26
0
0
0
0
0
3
8
12
32
55
1
4
4
46
55
0
0
0
6
6
0
1
0
8
9
0
0
0
0
0
0
0
1
3
4
0
0
1
7
8
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
21
39
56 106 222
36
79
93
54 262
2
6
18
13
39
6
15
27
23
71
5
14
27
17
63
0
0
0
10
10
3
5
15
45
68
0
0
1
5
6
0
0
0
‐4
‐4
0
0
1
5
6
6
8
17
39
70
3
4
16
46
69
0
1
0
5
6
0
1
0
8
9
0
0
0
‐2
‐2
91 120 147 170 528
88
51
17
4 160
14
12
7
0
33
23
23
8
1
55
16
15
8
1
40
0
1
0
6
7
0
3
0
17
20
0
0
0
0
0
0
1
0
8
9
0
0
0
0
0
59
82 118 148 407
74
71
47
12 204
2
2
3
0
7
10
19
22
3
54
72
71
47
12 202
10
15
21
62 108
14
29
54
77 174
0
3
5
13
21
0
3
5
13
21
0
4
7
15
26
3
0
3
15
21
5
8
16
55
84
1
0
1
21
23
0
0
0
‐1
‐1
0
0
0
0
0
1
2
2
18
23
1
1
2
21
25
0
0
0
0
0
0
0
0
4
4
1
2
3
35
41
0
3
3
8
14
7
15
19
51
92
1
5
3
12
21
0
1
0
4
5
0
0
0
3
3
10
7
20
52
89
16
27
58
73 174
1
1
10
18
30
4
3
16
24
47
0
0
0
‐5
‐5
0
0
0
4
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
123 153 174 179 629
25
0
0
0
25
‐76 ‐33
‐4
0 ‐113
28
1
0
0
29
39
1
0
0
40
8
16
21
70 115
18
44
87
79 228
7
2
7
14
30
6
2
4
12
24
7
2
7
12
28
1
0
0
9
10
3
0
4
26
33
1
0
0
3
4
0
0
0
‐2
‐2
1
0
0
4
5
5
6
7
21
39
4
5
11
29
49
1
0
0
5
6
1
2
4
10
17
1
2
4
9
16
3
5
5
31
44
4
2
18
51
75
0
0
0
3
3
0
1
2
21
24
0
0
1
6
7
164 178 178 180 700
2
0
0
0
2
0
0
0
0
0
‐13
‐3
‐2
‐2 ‐20
0
0
0
0
0
0
0
1
3
4
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
6
9
0
1
0
8
9
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
4
5
3
2
23
33
1
2
0
11
14
0
1
0
3
4
0
1
0
1
2
Not Estimated
0
0
0
5
5
1
0
0
18
19
0
0
0
‐1
‐1
0
0
0
1
1
0
0
0
2
2
0
0
2
2
4
0
0
0
6
6
0
0
0
1
1
0
0
0
‐1
‐1
0
0
0
0
0
64 104 119 161 448 119
81
20
6 226
‐8 ‐18
‐8
‐3 ‐37
6
13
2
1
22
0
0
0
0
0
27
52
74 107 260
90 103 108
42 343
6
17
33
14
70
2
6
12
3
23
0
0
0
0
0
1
2
2
17
22
2
4
4
46
56
0
0
0
3
3
0
0
0
3
3
0
0
0
1
1
4
4
8
67
83
2
10
35
70 117
0
1
1
6
8
0
1
1
6
8
0
0
0
0
0
3
3
6
33
45
0
2
1
23
26
0
0
0 ‐13 ‐13
0
0
1
15
16
0
0
0
0
0
2
7
12
37
58
14
13
39
68 134
2
1
4
27
34
0
1
2
8
11
0
1
2
10
13
35
59
79 147 320
29
85
73
17 204
‐1 ‐11 ‐52 ‐19 ‐83
‐1
‐5 ‐29
‐6 ‐41
0
0
0
0
0
6
9
11
47
73
11
8
36
58 113
2
0
2
18
22
3
0
10
27
40
0
0
0
0
0
0
0
0
9
9
0
0
0
3
3
0
0
0
‐1
‐1
0
0
0
0
0
0
0
0
0
0
2
1
5
24
32
4
4
18
66
92
0
1
0
12
13
0
0
0
3
3
0
0
0
0
0
47
72
91 130 340 103
90
67
32 292
33
31
25
13 102
6
6
8
5
25
25
25
20
12
82
0
1
0
2
3
0
0
1
1
2
0
0
0
0
0
0
2
1
2
5
0
0
0
1
1
0
0
0
7
7
0
0
1
17
18
0
0
0
‐3
‐3
0
0
1
12
13
0
0
0
0
0
3
3
1
22
29
6
3
17
51
77
1
1
2
11
15
2
2
2
17
23
0
0
0
0
0
12
16
31
73 132
27
59
88
83 257
3
5
19
27
54
7
15
29
38
89
0
0
0
0
0
0
0
0
4
4
0
0
0
9
9
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
12
26
35
87 160
18
46
66
68 198
0
5
6
13
24
1
7
9
18
35
26
53
81
73 233
160 168 178 178 684
0
0
0
0
0
0
0
0
0
0
‐1
‐3
0
0
‐4
0
0
0
0
0
54
81 115 143 393
99
76
49
22 246
22
29
18
10
79
15
24
15
7
61
0
0
0
0
0
9
11
14
39
73
23
39
58
88 208
6
6
12
34
58
2
0
3
16
21
1
0
2
12
15
46
67 100 127 340 129 105
74
23 331
20
29
34
6
89
0
‐6
‐6
‐9 ‐21
0
0
0
0
0
3
2
1
13
19
0
0
1
13
14
0
0
0
0
0
0
0
0
‐1
‐1
0
0
0
0
0
0
0
2
4
6
3
4
4
15
26
0
1
0
3
4
0
1
0
3
4
0
0
0
0
0
58
87 118 154 417 116
73
41
17 247
20
19
16
5
60
14
18
13
4
49
0
0
0
0
0
12
11
32
65 120
20
23
54
66 163
2
4
8
8
22
6
6
24
28
64
0
0
0
0
0
9
5
10
37
61
2
7
9
62
80
0
0
0
10
10
0
0
0
10
10
0
0
0
0
0
2
9
12
35
58
5
15
30
76 126
0
0
1
16
17
0
0
0
7
7
0
0
0
0
0
24
explanation–perhaps ethnic clustering provides a more easily accessible supply of workers skilled in the
preparation of a particular cuisine–I would argue for a demand-side interpretation. A restaurant requires
far more customers than employees and it is much easier for a few employees to commute to a different
neighborhood than to move the customer base. From the perspective of the restaurant owner it would seem
that consumer location should weigh more heavily than employee location.
I use the Moran’s I measure of spatial auto-correlation to capture the general clustering/dispersion of an
ethnic population in a city. Specifically, I count the number of people born in each country in each census
tract with 2000 Census data and then calculate the correlation between neighboring tracts:
⎞⎛ N N
⎞
⎛
⎜
⎜
I=⎜
⎜
⎝
⎟ ⎜ ∑ ∑ wi j (Xi − X̄)(X j − X̄) ⎟
⎟ ⎜ i=1 j=1
⎟
⎟⎜
⎟
⎟⎜
⎟
N
N
⎠⎝
⎠
2
∑ wi j
∑ (Xi − X̄)
N
N
∑
i=1 j=1
(23)
i=1
In equation 23 Xi and X j represent the ethnic population in two neighboring tracts where X̄ is the average
across all tracts. The weights matrix wi j is a matrix of 1’s and 0’s indicating whether two tracts are neighbors33 ; N is the total number of tracts in a city. I calculate this measure for each ethnicity in each city; if
a city does not have any people of that ethnicity I cannot calculate the statistic and drop that city-cuisine
pair from this analysis34 . The Moran’s I is a measure of correlation and thus ranges from -1 to 1 with an
−1
when there is no spatial autocorrelation. It is important to note that the expected
expected value of N−1
value of Moran’s I does not depend on X and thus cities with a greater percentage of people from a given
ethnicity do not necessarily have a greater Moran’s I. Many of the cities in the lower land quartiles have few
census tracts and so I restrict the analysis to the 182 cities of the top land quartile. In Table 7 I break up each
ethnic cuisine into cities with a restaurant of that cuisine and cities without and show the average percentage
of people from that ethnicity and the average Moran’s I for each group. Even when limiting to the top land
quartile some cities have too few people from a given ethnicity to calculate the spatial distribution and so not
all cuisines will have 182 cities listed. From the table it is clear that cities with a restaurant of a given ethnic
cuisine tend to have a greater percentage of people from that ethnicity as well as a much higher Moran’s I,
indicating greater spatial correlation of residential location.
In order to separate the effect of the size of the ethnic population from the spatial distribution of that
population I re-run the pooled logit specification shown in Table 3, adding in the Moran’s I statistic and again,
restricting to the top land quartile. In the first column of panel A of Table 8 I run the previous specification
on the reduced sample and obtain similar results to column 8 of Table 3. Turning to column 2, the Moran’s I
statistic is quite significant and somewhat reduces the magnitude of the coefficient on population, land, and
ethnicity. It is difficult to compare the magnitudes of these coefficients but since Moran’s I ranges from −1
to 1 and ethnic percentage from 0 to 1 a rough approximation is that a 1% increase in the percentage of the
population belonging to a given ethnicity increases the likelihood of a city having that cuisine by the same
amount as a .03 increase in the spatial correlation of that population. In other words, bringing the ethnic
population of a city closer together can achieve the same result as increasing the size of that population.
These results show an effect of spatial concentration but do not imply that this effect comes from reduced transportation cost to a restaurant. To show the proximity of restaurants to ethnic concentrations I
estimate the probability a particular census tract has a restaurant of cuisine v on measures of the census
tract population of ethnicity v. I take the set of all census tracts with a restaurant for every city and pool all
33 I used the ”Queen” adjacency definition–named after the chess piece’s movement–so that two tracts are neighbors if they have
any shared borders.
34 I used the ”spdep” package in R to run the analysis.
25
ethnic cuisines, removing cuisines with too few observations to be estimated, and include controls, cuisine
fixed effects, and city fixed effects. Column 1 of Panel B shows that census tracts with larger populations of
ethnicity v are more likely to have a corresponding restaurant while column 2 shows the same thing using the
percentage of the census tract population in ethnicity v. I also estimated separate linear probability models
for each ethnic cuisine (not shown) and found that 38 of the 40 cuisines had a positive coefficient on census
tract ethnic population with 23 of these cuisines having statistically significant coefficients35 . The proximity
of ethnic populations to ethnic restaurants argues against variety being completely driven by gourmands.
Taken together, these estimates show that more concentrated ethnic populations increase the likelihood of a
city having a restaurant of the corresponding cuisine and that these restaurants are often located close to the
corresponding populations.
5
Conclusion
I have argued that variety in the restaurant market results from the aggregation of specific tastes from a
heterogeneous population. The importance of transportation cost in restaurant consumption implies that the
spatial distribution of demand is a key determinant of whether a given variety can exist in the market. Cities
that concentrate a large population into a small area increase the mass of consumers demanding specific
varieties and thereby increase the likelihood a firm finds sufficient demand for its product. The pattern of
cuisines across US cities follows a fairly regular hierarchical distribution that indicates a similarity in tastes
across cities. Further, larger and denser cities have both greater variety and rarer varieties of restaurants.
Varieties that appeal to fewer people are much more likely to be found in denser cities because spatial aggregation becomes more important when demand is limited. The presence of ethnic neighborhoods or other
geographic clustering of tastes facilitates the spatial aggregation of demand and can significantly increase
the likelihood a market supports a particular variety. Overall, the results in this paper show a link between
city structure and product differentiation and provide empirical evidence for one of the important consumer
benefits of agglomeration.
35 I
dropped ethnic cuisines where the estimated model failed the F test. Two of the cuisines had negative but statistically
insignificant coefficients on ethnic population size. I also estimated separate models using ethnic population percentage, with very
similar results.
26
Table 7: Ethnic clustering with matched cuisines
Cuisine
Afghan
Afghan
African
African
American (New)
American (New)
American (Traditional)
American (Traditional)
Argentinean
Argentinean
Armenian
Armenian
Asian
Asian
Austrian
Austrian
Belgian
Belgian
Brazilian
Brazilian
Burmese
Burmese
Cambodian
Cambodian
Caribbean
Caribbean
Central European
Central European
Chilean
Chilean
Chinese
Chinese
Colombian
Colombian
Cuban
Cuban
Dim Sum
Dim Sum
Eastern European
Eastern European
Egyptian
Egyptian
English
English
Ethiopian
Ethiopian
Filipino
Filipino
French
French
German
German
Greek
Greek
Hungarian
Hungarian
Indian
Indian
Indonesian
Indonesian
Has Restaurant
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
City Count
99
9
160
20
63
119
9
173
144
10
79
2
54
128
159
1
159
7
147
21
138
2
133
4
121
59
177
5
147
3
4
173
165
9
141
30
175
2
169
13
158
3
158
24
118
11
176
6
69
111
124
58
56
108
162
3
74
106
142
10
Ethnic %
0.057%
0.183%
0.341%
0.707%
87.408%
85.081%
93.064%
85.513%
0.053%
0.118%
0.024%
4.844%
2.534%
5.085%
0.028%
0.084%
0.036%
0.049%
0.105%
0.109%
0.030%
0.251%
0.099%
0.231%
0.257%
1.981%
0.650%
2.481%
0.041%
0.067%
0.000%
0.453%
0.193%
0.598%
0.183%
0.457%
0.419%
2.509%
0.638%
1.511%
0.047%
0.127%
0.292%
0.289%
0.038%
0.120%
0.671%
3.125%
0.048%
0.075%
0.278%
0.311%
0.042%
0.067%
0.035%
0.096%
0.327%
0.643%
0.042%
0.092%
Moran's I
‐0.016
0.072
0.034
0.236
0.041
0.146
‐0.021
0.117
‐0.016
0.022
‐0.006
0.538
0.123
0.230
0.001
0.322
‐0.009
0.110
0.004
0.094
‐0.001
0.176
0.025
0.188
0.011
0.150
0.065
0.449
‐0.013
0.078
‐0.088
0.072
0.015
0.237
0.001
0.143
0.065
0.355
0.052
0.374
‐0.004
0.182
0.039
0.228
0.006
0.096
0.094
0.502
0.028
‐0.028
0.046
0.020
0.172
‐0.049
0.053
‐0.004
0.296
0.016
0.153
0.001 27
0.129
Cuisine
Irish
Irish
Italian
Italian
Jamaican
Jamaican
Japanese
Japanese
Korean
Korean
Lebanese
Lebanese
Malaysian
Malaysian
Mediterranean
Mediterranean
Mexican
Mexican
Middle Eastern
Middle Eastern
Moroccan
Moroccan
Noodle Shop
Noodle Shop
Latin American
Latin American
Polish & Czech
Polish & Czech
Polynesian
Polynesian
Portuguese
Portuguese
Puerto Rican
Puerto Rican
Russian
Russian
Scandinavian
Scandinavian
South American
South American
Spanish
Spanish
Sushi
Sushi
Swiss
Swiss
Thai
Thai
Tibetan
Tibetan
Turkish
Turkish
Venezuelan
Venezuelan
Vietnamese
Vietnamese
Pan‐Asian & Pacific Rim
Pan‐Asian & Pacific Rim
Has Restaurant
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
City Count
130
39
11
167
157
6
31
148
118
62
140
18
139
8
129
52
3
179
109
70
144
9
156
21
151
31
174
3
91
5
135
3
179
3
170
5
167
2
165
17
127
36
132
47
158
8
45
128
175
2
150
7
152
4
93
87
143
39
Ethnic %
0.042%
0.079%
0.053%
0.127%
0.228%
0.594%
0.049%
0.223%
0.258%
0.653%
0.046%
0.786%
0.027%
0.057%
0.252%
0.289%
0.505%
4.952%
0.230%
0.903%
0.033%
0.072%
0.307%
1.447%
6.594%
9.499%
0.135%
0.955%
0.035%
0.043%
0.064%
0.054%
0.436%
1.851%
0.126%
0.436%
0.038%
0.053%
0.678%
1.037%
0.032%
0.060%
0.185%
0.214%
0.035%
0.063%
0.029%
0.106%
0.389%
5.120%
0.035%
0.058%
0.082%
0.106%
0.213%
0.904%
3.521%
7.291%
Moran's I
‐0.013
0.067
‐0.114
0.046
0.017
0.288
‐0.018
0.076
0.037
0.192
0.012
0.139
0.003
0.125
0.001
0.151
‐0.148
0.187
0.017
0.166
‐0.013
0.144
0.048
0.222
0.173
0.354
0.024
0.302
‐0.015
0.059
0.003
0.115
0.041
0.412
0.035
0.369
0.004
0.153
0.034
0.278
‐0.040
0.031
0.033
0.134
‐0.004
0.006
‐0.060
0.045
0.064
0.464
‐0.007
0.121
‐0.007
0.113
0.011
0.201
0.161
0.334
Table 8: Likelihood of having a given cuisine with clustered ethnic populations
Panel A: Census place level
Cuisine Indicator
Coefficients (marginal effects)
Pop 2007‐8 (logs)
Land sq mtrs (logs)
Average HH Size
Median HH income (000's)
%Old (>64)
%Young (<35)
%College grad
%Corresponding Ethnicity
0.1327***
[0.0057]
‐0.0422***
[0.0071]
‐0.0821**
[0.0317]
‐0.0007
[0.0008]
‐0.0701
[0.2813]
‐0.047
[0.1865]
0.3032***
[0.072]
0.4277***
[0.0893]
Moran's I
Cuisine Fixed Effects
Cuisine Indicator
YES
0.1196***
[0.006]
‐0.0367***
[0.0072]
‐0.0800** [0.031]
‐0.0007
[0.0008]
‐0.067
[0.2817]
‐0.0468
[0.186]
0.3073***
[0.0711]
0.3723***
[0.0939]
0.1358***
[0.0222]
YES
Observations
9790
9790
Pseudo R‐squared
0.634
0.639
Clustered standard errors in brackets (182 clusters)
*** p<0.01, ** p<0.05, * p<0.1
Panel B: Census tract level
Cuisine Indicator
Coefficients (OLS)
Corresponding ethnic population (000's)
Remaining population (000's)
Average HH Size
Median HH income (000's)
%Old (>64)
%Young (<35)
%College grad
0.024***
[0.002]
0.002***
[0.000]
‐0.028***
[0.003]
‐0.000**
[0.000]
0.034***
[0.006]
0.028***
[0.006]
‐0.025*
[0.015]
%Corresponding Ethnicity
Constant
0.053***
[0.008]
Cuisine Fixed Effects
YES
Census Place Fixed Effects
YES
Observations
959753
R‐squared
0.236
Robust standard errors in brackets (726 clusters)
*** p<0.01, ** p<0.05, * p<0.1
Cuisine Indicator
‐0.027***
[0.003]
‐0.000**
[0.000]
0.038***
[0.006]
0.035***
[0.006]
‐0.023
[0.016]
0.292***
[0.015]
0.051***
[0.008]
YES
YES
959753
0.237
References
A NDERSON , S. P., A.
tiation. MIT Press.
DE
PALMA ,
AND
J.-F. T HISSE (1992): Discrete Choice Theory of Product Differen-
B ERRY, S., AND J. WALDFOGEL (2010): “Product Quality and Market Size,” The Journal of Industrial
Economics, 58(1), 1–31.
B RAKMAN , S., AND B. J. H EIJDRA (2004): The Monopolistic Competition Revolution in Retrospect. Cambridge Press.
B RESNAHAN , T. F., AND P. C. R EISS (1991): “Entry and Competition in Concentrated Markets,” Journal
of Political Economy, 99.
C AMPBELL , J. R.,
nomics, 53.
AND
H. A. H OPENHAYN (2005): “Market Size Matters,” Journal of Industrial Eco-
C HEN , Y., AND S. ROSENTHAL (2008): “Local amenities and life-cycle migration: Do people move for
jobs or fun?,” Journal of Urban Economics, 64(3), 519–537.
C HRISTALLER , W., AND C. BASKIN (1966): Central places in southern Germany. Prentice-Hall.
C OMBES , P., G. D URANTON , AND L. G OBILLON (2011): “The identification of agglomeration economies,”
Journal of Economic Geography, 11(2), 253–266.
D IXIT, A. K., AND J. E. S TIGLITZ (1977): “Monopolistic Competition and Optimum Product Diversity,”
American Economic Review.
F UJITA , M., T. M ORI , V. J. H ENDERSON , AND Y. K ANEMOTO (2004): “Spatial Distribution of Economic
Activities in Japan and China,” Handbook of Regional and Urban Economics, 4.
28
G LAESER , E., AND J. G OTTLIEB (2009): “The Wealth of Cities: Agglomeration Economies and Spatial
Equilibrium in the United States,” Journal of Economic Literature, 47(4), 983–1028.
G LAESER , E. L., J. KOLKO , AND A. S AIZ (2001): “Consumer City,” Journal of Economic Geography.
H SU , W. (2011): “Central place theory and city size distribution,” Economic Journal (forthcoming).
I RMEN , A., AND J. T HISSE (1998): “Competition in multi-characteristics spaces: Hotelling was almost
right,” Journal of Economic Theory, 78(1), 76–102.
L EE , S. (2010): “Ability sorting and consumer city,” Journal of Urban Economics, 68(1), 20–33.
L ÖSCH , A. (1967): The economics of location. New York, John Wiley.
M AZZEO , M. (2002): “Product choice and oligopoly market structure,” The Rand Journal of Economics,
33(2), 221–242.
M AZZOLARI , F., AND D. N EUMARK (2010): “Immigration and product diversity,” Journal of Population
Economics, pp. 1–31.
M ORI , T., K. N ISHIKIMI , AND T. S MITH (2008): “The Number-Average Size Rule: A New Empirical
Relationship between Industrial Location and City Size,” Journal of Regional Science, 48(1), 165–211.
S ALOP, S. C. (1979): “Monopolistic competition with outside goods,” Bell Journal of Economics, 10.
S YVERSON , C. (2004): “Market Structure and Productivity: A Concrete Example,” Journal of Political
Economy, 112.
TABUCHI , T. (2009): “Hotelling’s Spatial Competition Reconsidered,” CIRJE F-Series.
WALDFOGEL , J. (2008): “The median voter and the median consumer: Local private goods and population
composition,” Journal of Urban Economics, 63(2), 567–582.
29
6
Appendix
6.1
Multiple Firms
With multiple firms there are three possible equilibria, which I label following (Salop 1979): an equilibria
where firms compete with neighbors for consumers (”competitive”), an equilibria where firms are local monopolists but do not have a large enough market extent to set monopoly prices (”kinked”), and an equilibria
where each firm operates as a local monopolist in its market (”monopoly”). The equilibria are determined
by the distance from the firm to the indifferent consumer, who many now be indifferent between the reserve
good or the good of a competing firm. Let dm represent the distance to a consumer indifferent between the
product and the reserve good, dc the distance when a consumer is indifferent between two neighboring firms
setting equal prices in equilibrium, and n is the number of firms:
u1 − u0 − pm
τ
L
=
2n
dm =
(24)
dc
(25)
The land area in the market determines the price a firm sets, which in turn determines the distance to the
indifferent consumer. The competitive equilibrium has a symmetric Nash equilibrium with prices as a best
response to competing firms while in the monopoly equilibrium the firm chooses a price to maximize profit
given the reserve good. The kinked equilibrium price is found by equating dm = dc and solving for price.
pc = c +
τL
n
τL
2n
u1 − u0 + c
=
2
(26)
pk = u1 − u0 −
(27)
pm
(28)
When pc < pk then we must be in the competitive equilibrium since any firm charging pk would be undercut.
∗
Once land expands to L = 2n
3 L then pk becomes smaller than pc and we are in the kinked equilibrium; if
the firm tried to charge pc the consumer would consume their reserve good. The kinked equilibrium case
is very similar to the minimum entry condition for the single firm in that the firm would like to charge
the monopolist’s price but is constrained in geographic extent, this time by the presence of the other firms.
In fact, the kinked equilibrium frontier collapses to the minimum entry condition when n = 1. Finally, at
L = nL∗ there will be exactly n local monopolists charging the monopoly price of pm . For L > nL∗ there will
be a monopoly equilibrium with n firms but with gaps between the geographic market extents36 .
⎧ ∗ ∗ 2
N L n
∗

if L ≤ 2n
 L
3 L , ”full coverage, competitive equilibrium”




⎨
∗ L∗ n2
∗
∗
(29)
Nmin (n, L) = 2N
if 2n
2nL∗ −L
3 L < L ≤ nL , ”full coverage, kinked equilibrium”






⎩ 2N ∗ L
if nL∗ < L, ”partial coverage, local monopoly equilibrium”
L∗
6.2
Additional Estimation Results and Statistics
there are n firms in the market and L > nL∗ then the profit to the firms as monopolists with gaps is higher than the kinked
profit and thus charging the price pk < pm is not an equilibrium strategy.
36 If
30
Table 9: Cuisine-level Logit Model Estimaton
Cuisine
Number Cities
Pop 2007‐8 (logs)
2.104***
[0.487]
2.100***
[0.497]
1.408***
[0.216]
1.654***
[0.228]
1.891***
[0.531]
Afghan
17
African
27
American (New)
253
American (Traditional)
545
Argentinean
13
Armenian
2
Asian
322
Austrian
2
Bakeries
404
Barbecue
507
Belgian
7
Brazilian
34
Burmese
4
Cajun & Creole
148
Californian
134
Cambodian
5
Caribbean
96
Central European
7
Chilean
3
Chinese
670
Coffee Shops & Diners
373
Colombian
10
Cuban
43
Deli
600
Desserts
482
Dim Sum
4
Eastern European
21
Eclectic & International
155
Egyptian
3
English
37
Ethiopian
14
Filipino
9
French
272
German
85
Greek
227
Hamburgers
280
Health Food
68
Hot Dogs
55
Hungarian
4
Indian
222
Indonesian
10
Irish
70
Italian
528
Jamaican
7
Japanese
407
1.533***
[0.188]
1.845***
[0.187]
0.740***
[0.160]
6.360**
[2.698]
2.218***
[0.445]
1.696**
[0.860]
1.494***
[0.215]
1.653***
[0.241]
5.104**
[1.979]
1.466***
[0.263]
4.330***
[1.552]
2.450*
[1.340]
2.095***
[0.328]
1.353***
[0.163]
2.514***
[0.701]
2.803***
[0.475]
1.479***
[0.204]
1.246***
[0.160]
1.433*
[0.798]
2.315***
[0.497]
1.632***
[0.223]
2.271***
[0.433]
2.550***
[0.651]
3.017***
[0.809]
1.238***
[0.181]
1.344***
[0.258]
1.757***
[0.212]
1.697***
[0.183]
1.431***
[0.302]
1.099***
[0.265]
2.086**
[0.910]
1.958***
[0.233]
5.834***
[1.827]
1.143***
[0.275]
2.026***
[0.232]
1.829**
[0.721]
1.545***
[0.196]
Land sq mtrs (logs)
Av HH Size
‐1.113** ‐3.444**
[0.485]
[1.521]
‐0.618
‐0.905
[0.426]
[1.184]
0.034 ‐1.490***
[0.199]
[0.423]
0.253 ‐2.358***
[0.188]
[0.449]
‐0.649
‐1.468
[0.525]
[1.540]
‐0.193
[0.171]
‐0.364**
[0.163]
0.775***
[0.159]
1.544
[1.664]
‐0.597
[0.378]
‐1.189
[1.020]
‐0.252
[0.199]
‐0.299
[0.218]
‐3.661**
[1.758]
‐0.125
[0.248]
0.03
[1.205]
0.96
[1.766]
‐0.005
[0.239]
0.22
[0.151]
‐0.912
[0.640]
‐1.110***
[0.373]
‐0.011
[0.175]
0.094
[0.145]
‐0.968
[0.927]
‐1.313***
[0.457]
‐0.3
[0.206]
‐0.781**
[0.374]
‐1.001*
[0.600]
‐1.799**
[0.777]
‐0.079
[0.172]
‐0.02
[0.242]
‐0.184
[0.193]
‐0.358**
[0.164]
0.057
[0.276]
‐0.209
[0.260]
‐0.097
[0.962]
‐0.362*
[0.205]
‐1.181
[1.006]
‐0.185
[0.270]
‐0.293
[0.187]
0.224
[0.743]
‐0.087
[0.180]
Med HH Inc
0.025
[0.032]
‐0.041
[0.031]
0.019*
[0.010]
0.016
[0.011]
‐0.019
[0.040]
‐1.331*** 0.021**
[0.366]
[0.010]
‐1.294***
[0.359]
0.338
[0.337]
‐29.060*
[15.075]
‐1.868*
[1.086]
‐0.293
[2.081]
‐0.825*
[0.452]
‐2.323***
[0.549]
‐2.478
[4.121]
‐2.195***
[0.647]
‐15.335**
[6.448]
‐1.353
[6.774]
‐0.543
[0.553]
‐0.397
[0.334]
‐0.284
[1.955]
‐1.888*
[0.983]
‐1.739***
[0.407]
‐0.608*
[0.326]
1.693
[1.597]
‐1.404
[1.174]
‐2.571***
[0.515]
0.032***
[0.011]
‐0.025**
[0.011]
0.253
[0.254]
‐0.004
[0.024]
‐0.046
[0.068]
‐0.022*
[0.013]
0.042***
[0.012]
‐0.123
[0.131]
‐0.014
[0.017]
0.242**
[0.106]
‐0.313
[0.304]
‐0.019
[0.017]
‐0.005
[0.010]
‐0.006
[0.055]
0.027
[0.026]
0.004
[0.012]
0.003
[0.010]
‐0.098*
[0.059]
‐0.037
[0.035]
0.025**
[0.012]
‐3.618*** 0.048*
[1.231]
[0.027]
‐3.202
‐0.065
[2.157]
[0.053]
‐0.735
0.073
[1.648]
[0.055]
‐1.116*** ‐0.014
[0.396]
[0.011]
‐0.029
‐0.022
[0.566]
[0.019]
‐2.310*** ‐0.002
[0.460]
[0.012]
‐0.970*** 0.028***
[0.357]
[0.010]
0.053 ‐0.040**
[0.680]
[0.019]
‐1.336*
‐0.004
[0.702]
[0.018]
‐2.296
0.034
[4.056]
[0.095]
‐1.307*** ‐0.003
[0.432]
[0.012]
‐14.835** 0.239*
[6.207]
[0.123]
‐2.256*** 0.001
[0.699]
[0.017]
‐1.749*** 0.012
[0.447]
[0.013]
‐4.979
‐0.046
[3.201]
[0.074]
‐0.598
‐0.001
[0.380]
[0.011]
%College % Ethnicity
Grad
2.443
[3.336]
6.677**
[2.887]
1.236
[1.197]
‐1.102
[1.352]
5.318
[3.807]
‐1.836
[1.134]
0.685
[1.157]
3.732***
[1.244]
‐31.662
[22.646]
6.868***
[2.573]
2.83
[6.828]
4.148***
[1.397]
2.35
[1.431]
9.279
[8.518]
2.094
[1.667]
‐5.964
[10.947]
21.329
[15.726]
1.322
[2.065]
0.868
[1.132]
4.991
[5.778]
2.034
[2.800]
0.617
[1.469]
‐0.661
[1.118]
8.523*
[4.882]
4.064
[3.055]
1.685
[1.348]
317.656***
[116.301]
15.966
[44.266]
‐0.519
[1.075]
‐0.354
[1.179]
145.758
[96.582]
Cons.
‐1.809
[5.060]
‐14.944***
[5.129]
‐13.405***
[2.225]
‐13.827***
[2.706]
‐11.937*
[6.469]
Pseudo R‐Sq
Cuisine
0.37
Korean
108
0.47
Kosher
21
0.31
Lebanese
23
0.31
Malaysian
14
0.38
Mediterranean
89
Meat‐and‐Three
4
7.049*** ‐10.328*** 0.30
[1.928]
[1.931]
3588.876
[4526.048]
76.591***
[27.879]
424.601**
[201.424]
108.66
[122.119]
10.476***
[2.688]
85.129
[56.030]
537.512
[673.119]
55.773
[58.938]
31.352
[23.551]
21.028***
[5.544]
18.358
[12.318]
23.416
[14.585]
‐11.209***
[2.008]
‐20.802***
[2.260]
‐50.101*
[29.048]
‐16.006***
[4.585]
‐2.03
[11.933]
‐11.555***
[2.298]
‐11.645***
[2.400]
6.406
[16.645]
‐10.653***
[2.682]
‐33.705*
[17.891]
‐48.376
[29.369]
‐16.100***
[3.713]
‐16.862***
[2.063]
‐18.636**
[8.444]
‐12.694***
[4.101]
‐8.981***
[2.448]
‐12.046***
[1.959]
‐7.632
[12.014]
‐3.177
[4.878]
‐9.216***
[2.243]
Number Pop 2007‐8 Land sq Cities
(logs)
mtrs (logs)
Mexican
629
Middle Eastern
115
Moroccan
10
0.25
Noodle Shop
39
0.78
Latin American
44
0.47
Pizza
700
0.32
0.34
Polish & Czech
4
0.32
Polynesian
9
0.35
Portuguese
4
0.70
Puerto Rican
3
0.38
Russian
5
0.75
Scandinavian
4
0.69
Seafood
448
0.29
Soups
260
0.29
South American
22
0.47
Southern & Soul
83
0.48
Southwestern
45
0.24
Spanish
58
0.21
Steakhouse
320
0.29
Sushi
73
0.40
Swiss
9
0.34
Tapas / Small Plates
32
Thai
340
Tibetan
3
‐8.008** 0.41
‐1.251
44.204
[2.758]
[86.458]
[4.030]
8.673** 600.765** ‐9.144
0.59
[4.110]
[272.326] [7.257]
‐5.545
12.968*
‐7.372
0.45
[7.247]
[7.366]
[8.251]
5.012*** 310.642** ‐10.752*** 0.31
[1.264]
[125.870] [2.030]
‐1.408
136.048** ‐15.475*** 0.35
[1.989]
[64.209]
[3.014]
2.384* 255.460*** ‐11.478*** 0.38
[1.314]
[74.733]
[2.251]
‐11.336*** 0.29
0.253
[1.135]
[1.970]
‐20.165*** 0.41
6.601***
[1.941]
[3.533]
2.502
‐8.388*** 0.22
[1.875]
[2.909]
3.376
888.313 ‐26.690* 0.51
[10.907] [548.514] [14.434]
4.275*** 61.381*** ‐14.120*** 0.42
[1.349]
[13.247]
[2.394]
‐13.261 1128.759** ‐26.477* 0.78
[13.588] [462.489] [15.710]
2.082
‐50.102 ‐6.743** 0.25
[1.710]
[149.604] [2.819]
3.314** 136.550** ‐11.882*** 0.38
[1.494]
[61.515]
[2.455]
9.879
72.855** ‐21.136* 0.53
[6.009]
[33.279] [11.494]
3.621*** 508.449*** ‐14.631*** 0.41
[1.323]
[81.732]
[2.264]
31
Turkish
7
Vegan
29
Vegetarian
132
Venezuelan
4
Vietnamese
160
Fast Food
684
Coffeehouse
393
Pan‐Asian & Pacific Rim
73
Family Fare
340
Cheesesteak
19
Chowder
6
Ice Cream
417
Bagels
120
Donuts
61
Juices & Smoothies
58
Av HH Size
Med HH Inc
%College % Grad
Ethnicity
Cons.
Pseudo R‐Sq
1.821***
[0.280]
2.522***
[0.514]
1.381***
[0.436]
3.534***
[0.818]
1.968***
[0.313]
1.014
[0.705]
0.629***
[0.236]
2.238***
[0.301]
3.173***
[0.925]
1.490***
[0.413]
1.686***
[0.375]
2.307***
[0.430]
1.517**
[0.741]
1.713***
[0.559]
4.602**
[2.156]
‐0.455*
0.667
‐0.023
3.258* 56.679***‐16.127***
[0.242]
[0.504]
[0.016]
[1.714] [13.491] [2.866]
‐1.362*** ‐2.163*
0.027
‐3.429
‐2.694
[0.450]
[1.197]
[0.039]
[3.943]
[4.601]
0.113
‐2.367
0.021
2.626 517.796***‐18.184***
[0.427]
[1.486]
[0.034]
[3.641] [138.737] [5.529]
‐1.815***
0.913
0.008
5.032 1062.794** ‐18.405**
[0.645]
[1.401]
[0.041]
[5.241] [356.400] [7.747]
‐0.644** ‐1.812***
0
6.358*** ‐21.389 ‐10.424***
[0.285]
[0.663]
[0.016]
[1.755] [29.950] [3.032]
0.791
‐5.394
‐0.077
3.818
‐17.404
[0.778]
[4.284]
[0.137]
[10.032]
[12.385]
1.051***
0.167 ‐0.038*** 5.505*** 30.561***‐22.830***
[0.223]
[0.492]
[0.014]
[1.625]
[9.503] [3.188]
‐0.559**
‐0.882
0.008
3.380** 55.920***‐16.389***
[0.248]
[0.548]
[0.015]
[1.674] [18.351] [2.894]
‐0.171
‐6.006*
0.143*
‐6.422 1664.923**‐31.020**
[0.743]
[3.489]
[0.082]
[9.479] [691.472] [13.080]
‐0.366
‐0.798
‐0.01
6.092*** 75.376***‐13.916***
[0.381]
[0.881]
[0.020]
[2.329] [16.376] [4.124]
‐0.248
‐2.458** ‐0.007
5.524** 5.519** ‐13.689***
[0.333]
[1.003]
[0.023]
[2.311]
[2.134] [3.783]
‐0.185 ‐2.689*** 0.048** ‐7.746***
‐8.772*
[0.313]
[0.740]
[0.023]
[2.729]
[4.850]
0.232
‐3.95
0.065
2.342
77.399 ‐22.407
[0.978]
[3.550]
[0.063]
[8.816] [48.240] [14.216]
‐0.884
0.359
‐0.024
3.988
‐0.948
‐9.44
[0.579]
[1.364]
[0.044]
[4.478] [384.041] [7.200]
‐2.477
‐10.573
‐0.247
7.152
114.91 14.728
[1.809]
[7.769]
[0.177]
[10.095] [115.530] [18.377]
0.40
3.070**
[1.324]
2.316***
[0.856]
1.232***
[0.160]
1.542***
[0.174]
1.955***
[0.467]
1.710***
[0.291]
0.845***
[0.296]
2.256***
[0.363]
0.930***
[0.150]
1.611***
[0.298]
0.905*
[0.530]
2.407***
[0.472]
2.100***
[0.213]
1.157
[1.023]
2.189**
[0.855]
2.414***
[0.489]
2.200***
[0.282]
1.861**
[0.807]
1.902***
[0.273]
1.373***
[0.297]
2.176***
[0.213]
2.455***
[0.385]
1.659***
[0.172]
1.147***
[0.389]
2.629***
[0.786]
1.994***
[0.199]
1.471***
[0.246]
1.362***
[0.272]
1.624***
[0.295]
0.739
[1.339]
‐1.387
[0.936]
0.18
[0.148]
‐0.399**
[0.160]
‐0.578
[0.434]
‐0.249
[0.262]
0.373
[0.299]
‐0.876***
[0.309]
0.466***
[0.149]
‐0.357
[0.269]
0.504
[0.582]
‐0.794**
[0.390]
‐0.707***
[0.185]
0.398
[1.248]
1.547
[0.996]
‐0.784*
[0.412]
‐0.656***
[0.240]
0.245
[1.005]
‐0.437*
[0.239]
‐0.208
[0.257]
‐0.663***
[0.181]
‐1.042***
[0.331]
‐0.458***
[0.155]
‐0.095
[0.405]
‐1.179
[0.793]
‐0.466***
[0.170]
‐0.202
[0.228]
‐0.416
[0.255]
‐0.588**
[0.267]
0.70
‐4.873
[6.961]
‐1.312
[2.194]
‐1.200***
[0.340]
‐0.062
[0.337]
‐1.536
[1.291]
‐0.525
[0.581]
‐1.194
[0.893]
‐2.555***
[0.804]
‐1.510***
[0.353]
‐1.589**
[0.706]
‐1.117
[2.012]
‐1.916*
[1.118]
‐1.409***
[0.393]
‐7.024
[4.795]
‐5.546
[3.759]
‐3.002**
[1.317]
‐1.031*
[0.536]
‐0.66
[3.655]
‐1.426***
[0.544]
‐0.011
[0.643]
‐0.635*
[0.384]
‐2.842***
[0.779]
‐1.281***
[0.339]
‐4.097***
[1.376]
‐1.65
[2.569]
‐0.878**
[0.366]
‐2.277***
[0.597]
0.32
[0.561]
0.472
[0.577]
0.032
[0.204]
0.073
[0.069]
‐0.01
[0.010]
‐0.018
[0.011]
0.001
[0.031]
‐0.044**
[0.019]
‐0.03
[0.022]
‐0.001
[0.021]
0.011
[0.010]
‐0.019
[0.017]
0.019
[0.043]
0.029
[0.028]
0.035***
[0.011]
‐0.098
[0.120]
0.052
[0.089]
‐0.016
[0.027]
‐0.019
[0.015]
0.034
[0.081]
‐0.016
[0.015]
0.053**
[0.022]
0.050***
[0.013]
0.035**
[0.016]
0.025**
[0.010]
0.065**
[0.030]
0.026
[0.047]
0.028**
[0.011]
0.022*
[0.013]
‐0.013
[0.018]
0.009
[0.017]
1.774
[18.445]
‐6.643
[9.391]
0.921
[1.154]
1.123
[1.144]
4.055
[3.266]
1.878
[1.843]
4.829**
[2.149]
2.089
[2.113]
‐1.475
[1.101]
6.216***
[1.838]
3.918
[5.353]
1.316
[3.121]
1.385
[1.230]
12.105*
[6.939]
13.328
[10.917]
8.153***
[2.725]
7.757***
[1.684]
7.153
[10.208]
4.324***
[1.612]
‐1.927
[2.122]
3.552***
[1.294]
3.801**
[1.898]
‐0.769
[1.080]
‐5.2
[3.507]
7.44
[6.155]
2.711**
[1.223]
5.458***
[1.519]
2.814
[1.886]
2.659
[1.980]
260.064 ‐49.746*
[194.603] [27.265]
‐225.087 ‐4.913
[1499.573] [10.686]
‐12.015***
[1.965]
‐9.396***
[1.913]
2.358 ‐13.504**
[12.261] [5.204]
‐13.988***
[3.076]
‐16.326***
[3.666]
427.424*** ‐6.967**
[117.237] [3.218]
‐14.185***
[1.929]
7.964 ‐11.373***
[32.107] [2.936]
219.034 ‐23.932***
[710.303] [8.403]
‐13.700***
[4.440]
511.064***‐9.028***
[114.707] [2.056]
60.216* ‐11.857
[34.992] [16.926]
174.689 ‐56.377**
[1030.183] [22.524]
‐12.232**
[4.729]
‐13.670***
[2.684]
32.202 ‐35.556**
[78.595] [17.559]
154.942***‐12.336***
[23.136] [2.615]
‐9.224**
[3.573]
‐13.305***
[2.184]
4.561* ‐7.820**
[2.418] [3.089]
‐7.321***
[1.830]
‐5.928
[4.313]
‐14.966
[10.176]
‐12.495***
[2.107]
‐11.876***
[2.499]
‐11.404***
[3.000]
‐12.931***
[3.157]
0.37
0.43
0.55
0.39
0.44
0.31
0.44
0.66
0.43
0.42
0.27
0.39
0.25
0.66
0.30
0.24
0.25
0.39
0.43
0.34
0.44
0.24
0.37
0.29
0.43
0.38
0.60
0.63
0.50
0.43
0.47
0.49
0.19
0.42
0.42
0.25
0.22
0.45
0.36
0.36
0.23
0.25
Table 10: Count of Cities with each Cuisine, by Land Quartile
CUISINE
Afghan
MISS
1
2
3
African
MISS
1
2
3
4
American (New)
MISS
1
2
3
4
American (Traditional)
MISS
1
2
3
4
Argentinean
MISS
1
2
3
4
Armenian
MISS
Asian
MISS
1
2
3
4
Austrian
1
3
Bakeries
MISS
1
2
3
4
Barbecue
MISS
1
2
3
Belgian
MISS
1
2
3
Brazilian
MISS
1
2
3
4
Burmese
MISS
2
Cajun & Creole
MISS
1
2
3
4
Californian
MISS
1
2
3
4
Cambodian
MISS
1
2
3
Caribbean
MISS
1
2
3
4
LQ4 LQ3 LQ2
2
2
4
2
0
3
0
1
0
0
1
1
0
0
0
1
2
4
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
21
45
68
8
9
24
7
30
42
7
7
9
6
7
9
3
4
7
91 128 153
74 111 124
32
58
93
16
31
52
7
8
8
5
6
15
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
41
63
90
39
59
88
2
6
6
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
57
83 112
29
50
78
38
59
82
0
3
4
0
1
0
0
0
0
65 121 151
56 107 133
13
32
53
6
11
15
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
8
2
0
4
1
1
1
0
0
2
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
6
31
30
5
24
24
2
5
4
0
5
2
0
1
0
0
1
0
13
19
32
9
9
21
4
5
5
6
8
16
2
2
6
3
3
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
14
17
6
12
14
0
3
2
0
0
3
0
0
0
0
0
1
LQ1
9
6
2
2
2
20
17
10
5
5
1
119
50
95
32
24
19
173
166
136
97
42
46
10
4
5
5
3
1
2
2
128
126
22
10
6
3
1
1
0
152
134
116
18
9
1
170
160
108
52
6
7
3
4
2
2
21
5
9
5
9
6
2
2
1
81
66
23
25
16
1
70
46
28
44
18
7
4
2
1
1
0
59
49
16
15
7
2
CUISINE
Central European
MISS
1
2
3
4
Chilean
MISS
Chinese
MISS
1
2
3
4
Coffee Shops & Diners
MISS
1
2
3
Colombian
MISS
1
2
Cuban
MISS
1
2
3
4
Deli
MISS
1
2
3
Desserts
MISS
1
2
3
4
Dim Sum
MISS
1
Eastern European
MISS
1
2
3
4
Eclectic & International
MISS
1
2
3
4
Egyptian
MISS
1
2
English
MISS
1
2
3
4
Ethiopian
MISS
1
2
3
Filipino
MISS
1
French
MISS
1
2
3
4
German
MISS
1
2
3
4
Greek
MISS
1
2
3
4
LQ4 LQ3 LQ2 LQ1
CUISINE
0
0
2
5 Hamburgers
0
0
1
3 MISS
0
0
0
21
0
0
0
12
0
0
1
23
0
0
0
2 Health Food
0
0
0
3 MISS
0
0
0
31
148 169 175 178 2
147 169 174 178 4
10
19
31
66 Hot Dogs
6
6
5
29 MISS
1
3
1
91
1
1
0
4 Hungarian
42
72 106 153 MISS
25
42
67 129 1
24
49
81 123 Indian
1
0
0
10 MISS
0
0
0
41
0
0
1
92
0
0
1
83
0
0
0
14
0
0
0
2 Indonesian
4
2
7
30 MISS
4
0
4
19 1
1
1
1
12 2
0
0
0
10 Irish
0
0
1
3 MISS
0
1
1
01
119 147 163 171 2
118 146 163 171 3
5
7
8
32 Italian
0
1
0
8 MISS
0
0
0
21
76 107 137 162 2
76 105 133 161 3
1
6
17
40 4
1
3
8
24 Jamaican
0
0
0
5 MISS
0
0
0
41
1
0
1
22
1
0
0
2 Japanese
0
0
1
0 MISS
4
4
0
13 1
3
4
0
72
0
0
0
53
1
0
0
44
0
0
0
3 Korean
0
0
0
1 MISS
14
21
40
80 1
7
10
13
46 2
4
12
22
46 3
4
5
8
35 Kosher
1
4
4
25 MISS
1
2
4
18 1
0
0
0
32
0
0
0
14
0
0
0
1 Lebanese
0
0
0
1 MISS
3
5
5
24 1
2
5
2
16 2
1
1
2
12 4
0
1
1
6 Malaysian
0
0
1
2 MISS
0
0
0
11
2
1
0
11 2
1
1
0
8 Mediterranean
1
0
0
5 MISS
0
0
0
21
0
0
0
12
1
1
1
63
1
1
1
54
0
0
0
3 Meat‐and‐Three
32
52
77 111 MISS
28
44
67 110 1
2
4
5
19 3
7
8
14
33 Mexican
1
6
6
26 MISS
2
4
6
24 1
4
6
17
58 2
3
6
15
52 3
0
0
1
84
1
0
1
8 Middle Eastern
0
0
0
7 MISS
0
0
0
11
17
43
53 114 2
17
42
51 114 3
1
3
3
29 Moroccan
0
2
0
16 MISS
1
0
0
61
0
0
0
22
3
4
32
LQ4
30
15
15
1
0
3
1
2
0
0
3
3
0
0
0
0
21
20
1
5
1
0
0
0
0
0
6
6
0
0
0
91
83
26
13
3
3
0
0
0
0
59
56
6
7
1
1
10
10
0
0
0
3
3
0
0
0
1
1
0
0
0
0
0
0
0
10
7
0
2
1
1
0
0
0
0
123
119
18
7
0
0
8
8
0
1
0
1
0
0
0
1
0
LQ3
51
21
36
4
0
5
3
2
0
0
8
5
4
0
0
0
39
37
6
4
0
0
0
0
0
0
8
5
2
1
0
120
116
40
26
10
4
1
0
1
0
82
81
10
9
1
1
15
15
1
0
0
0
0
0
0
0
2
1
1
0
0
3
3
0
0
7
4
1
2
2
0
0
0
0
0
153
151
38
12
1
0
16
13
5
0
0
0
0
0
0
0
0
LQ2
73
31
49
4
0
6
3
3
0
0
12
8
4
1
0
1
56
54
11
4
1
0
0
0
0
0
17
14
0
3
0
147
137
73
51
17
3
0
0
0
0
118
117
13
17
1
4
21
21
1
1
0
3
3
0
0
0
2
1
1
0
0
3
2
1
0
20
18
0
2
0
2
0
0
0
0
174
168
73
18
1
0
21
18
3
2
0
0
0
0
0
0
0
LQ1
126
85
83
13
2
54
28
34
3
1
32
21
16
3
3
0
106
103
31
19
4
2
10
9
2
1
39
31
14
5
2
170
167
124
90
36
20
6
2
4
1
148
145
35
49
22
9
62
60
10
7
2
15
14
3
2
1
18
6
10
3
1
8
4
3
2
52
45
14
21
12
6
4
2
3
1
179
178
115
59
18
2
70
60
26
10
2
9
3
2
5
1
1
CUISINE
Noodle Shop
MISS
1
2
Latin American
MISS
1
2
3
4
Pizza
MISS
1
2
3
4
Polish & Czech
MISS
1
Polynesian
MISS
1
3
Portuguese
MISS
1
2
Puerto Rican
MISS
1
2
Russian
MISS
1
2
4
Scandinavian
MISS
2
Seafood
MISS
1
2
3
4
Soups
MISS
1
South American
MISS
1
2
3
4
Southern & Soul
MISS
1
2
3
4
Southwestern
MISS
1
2
3
4
Spanish
MISS
1
2
3
4
Steakhouse
MISS
1
2
3
4
Sushi
MISS
1
2
3
Swiss
MISS
2
Tapas / Small Plates
MISS
1
2
3
LQ4
5
5
1
0
3
2
1
0
0
0
164
154
63
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
64
59
9
11
6
3
27
27
0
1
1
0
0
0
0
4
4
0
0
0
0
3
3
0
0
0
0
2
1
0
1
0
0
35
26
1
1
7
5
6
4
0
3
0
0
0
0
2
1
0
1
0
LQ3
6
5
2
0
5
4
1
0
0
0
178
171
93
2
0
0
0
0
0
3
3
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
104
92
8
25
5
4
52
52
0
2
0
1
0
1
0
4
4
0
0
0
0
3
3
0
0
0
0
7
5
0
1
0
1
59
44
1
2
21
4
9
8
1
0
1
0
0
0
1
0
1
0
0
LQ2
7
6
2
0
5
1
3
1
2
0
178
176
127
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
119
106
24
37
8
8
74
74
0
2
2
0
0
0
0
8
7
1
1
0
0
6
6
0
0
0
0
12
9
0
3
0
0
79
55
0
3
31
4
11
9
2
1
1
0
0
0
5
4
0
1
0
LQ1
21
18
10
3
31
16
13
11
8
5
180
180
154
17
2
1
3
2
2
6
0
4
3
3
3
0
1
3
1
1
2
5
4
1
3
1
2
0
2
161
141
77
90
36
25
107
107
2
17
7
11
6
1
1
67
65
14
6
2
3
33
23
8
8
4
1
37
34
6
10
8
3
147
131
9
17
83
32
47
36
10
13
9
9
8
1
24
14
6
13
4
CUISINE
Thai
MISS
1
2
3
4
Tibetan
MISS
1
2
Turkish
MISS
1
2
3
Vegan
MISS
1
2
3
Vegetarian
MISS
1
2
3
4
Venezuelan
MISS
1
2
3
Vietnamese
MISS
1
2
3
4
Fast Food
MISS
1
2
Coffeehouse
MISS
1
2
3
Pan‐Asian & Pacific Rim
MISS
1
2
3
4
Family Fare
MISS
1
2
3
Cheesesteak
MISS
1
3
Chowder
MISS
1
2
3
4
Ice Cream
MISS
1
2
Bagels
MISS
1
2
Donuts
MISS
1
Juices & Smoothies
MISS
1
LQ4
47
46
5
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
12
10
4
2
2
0
0
0
0
0
0
12
9
2
1
0
0
160
102
122
2
54
13
51
0
0
9
3
2
4
0
1
46
20
20
7
0
3
3
0
0
0
0
0
0
0
0
58
17
47
0
12
3
9
0
9
7
2
2
0
2
LQ3
72
71
5
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
2
0
16
11
7
2
1
0
0
0
0
0
0
26
23
3
2
0
0
168
133
132
2
81
16
77
0
0
11
5
3
2
1
2
67
42
29
14
0
2
1
1
0
0
0
0
0
0
0
87
21
77
0
11
2
9
0
5
5
0
9
2
7
LQ2
91
86
10
7
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
31
24
6
7
0
0
0
0
0
0
0
35
31
5
3
1
0
178
162
148
3
115
28
112
0
0
14
9
1
0
3
2
100
53
59
33
1
1
0
1
0
2
1
1
0
1
0
118
34
104
1
32
8
24
0
10
10
0
12
7
6
LQ1
130
128
29
14
1
3
2
0
1
1
7
5
3
2
1
22
10
18
7
3
73
65
33
20
8
3
4
1
1
2
2
87
85
20
12
4
5
178
173
160
27
143
71
132
8
2
39
24
15
19
10
17
127
102
85
60
1
13
10
3
1
4
2
2
1
1
2
154
71
142
2
65
37
39
1
37
37
5
35
26
16