Cities and Product Variety
Nathan Schiff∗
May 2013†
Abstract
This paper measures horizontal differentiation in the restaurant industry and argues 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, suggesting that larger, and
denser, markets will have greater variety in a manner consistent with the Central Place Theory of cities.
I 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 and population density with the
rarest cuisines found only in the densest cities. The results are consistent across multiple specifications
and when instrumenting for population density. 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. These findings parallel empirical results from Central Place Theory work on industrial composition
and provide evidence that demand aggregation has a significant impact on consumer product variety.
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 consumer product variety in
cities and therefore cannot explain why some cities seem to have more variety than others. Cities vary widely
in the characteristics of their residents, government, and culture and it could be that these idiosyncratic features explain all differences in consumer product variety. On the other hand, the Central Place Theory of
cities suggests a hierarchical pattern in the number of goods available in different size markets with larger
markets having all of the goods of smaller markets as well as additional higher order goods (Christaller
∗ Assistant
Professor, Sauder School of Business, University of British Columbia [email protected]
Kristian Behrens, James Campbell, Tianran Dai, Tom Davidoff, Andrew Foster, Martin Goetz,
Juan Carlos Gozzi, Vernon Henderson, Toru Kitagawa, Brian Knight, 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, Tsinghua University, City University of Hong Kong, Shanghai University of Finance and
Economics, and participants at the CUERE, IIOC, and UEA conferences for helpful comments.
† I thank Nathaniel Baum-Snow,
1
and Baskin 1966, Lösch 1967). While this theory has not been applied to consumer product variety, recent empirical work has shown that industrial composition varies systematically with population size (Mori,
Nishikimi, and Smith 2008, Hsu 2012, Mori and Smith 2011). In this paper I will show that a key feature of
the Central Place Theory of cities, demand aggregation, suggests that even if all cities were identical in their
characteristics, differences in population size and land area could lead to significant differences in consumer
product variety. I will argue that cities aggregate demand on two margins–population size (scale) and land
area (transportation cost)–and thus by concentrating groups of consumers with the same preferences in a
small geographic space, large, dense cities provide the necessary demand for a firm catering to that taste.
I then measure product variety across a large set of cities for an important non-tradable consumption
amenity—restaurants—and examine how demand aggregation affects variety across locations. Using a
unique data set of over 127,000 restaurants across 726 US cities I find that for large cities, population size,
land area, and the geographic clustering of specific populations have a substantial effect on the amount of
product variety in a city. For the 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 can be thought of as an increase in population density holding constant population size–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.
The way in which variety increases with population and land area is consistent with a simple model
of demand aggregation and many of the characteristics of the distribution of cuisines across cities parallel
findings from the empirical work on Central Place Theory. Bigger, denser cities have more cuisines but the
distribution of restaurants across cuisines, or evenness, declines with city size. The specific cuisines found in
each city follow a hierarchical structure in which cities with relatively rare cuisines often have all of the more
common cuisines and cities with few cuisines tend to have only common cuisines. Rare cuisines are only
found in cities with many restaurants while common cuisines can be found in cities with few restaurants.
These findings cannot be explained by the empirical distribution of restaurants across cuisines (“balls and
bins” models) and suggest that the demand aggregation mechanism of Central Place Theory can have a
significant effect on a city’s consumer product variety.
1.1
Consumer Cities and Non-tradable Product Variety
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 city1 . 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
1 Handbury
and Weinstein (2012) show that residents of cities also have greater access to tradable varieties and use a varietyadjusted price index to calculate the welfare effects of this greater access.
2
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 products2 . While this view
of variety has been quite useful in tackling many economic problems3 , it is less suitable 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-categories4 ; 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 uncontroversial5 . Moreover, transportation costs are often significant in the
decision to eat at a restaurant6 , a factor that could make the variety in cities different from that in places
with more dispersed populations. Conveniently, 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. And finally, restaurants are arguably one of the most prominent and important examples
of a city’s not-tradable consumer goods7 .
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.
2 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).
3 One prominent example is the new economic geography, see (Fujita, Mori, Henderson, and Kanemoto 2004).
4 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.”
5 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.
6 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.
7 Couture (2013) estimates the consumption benefit of greater access to restaurants, both across and within MSAs, and finds
large differences when comparing the most dense areas to the least dense.
3
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
12
14
Pop 2007-8 (logs)
Log #Cuisines
#C
((m1))
Slope=1.01, RSq=.86, results for 726 Census Places
1.2
10
16
Fitted values
Slope=.49, RSq=.67, results for 726 Census Places
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
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
differentiation8 .
8 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
4
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 relate my findings to Central Place Theory. 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 firms9 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
“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 a simple model with the
objective of showing how the two dimensions of demand aggregation–population and population density–
can affect variety even when all cities have identical characteristics. I base this model on Salop’s circular
city model of monopolistic competition but rather than normalizing population and land to one I keep these
as separate parameters. I add cuisine-specific entry thresholds in the spirit of (Bresnahan and Reiss 1991)10
to define the minimum conditions that would allow the first firm of a cuisine to enter the market. I then map
the Mobil and Zagats guides, while I am concerned with the entire range of cuisines, but not quality.
9 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.
10 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).
5
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 equlibrium11 . 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 competition12 .
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 city13 nor within city location patterns14 . Narrowing my aims to this objective allows me to make the
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 in the empirical
section.
11 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.
12 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.
13 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.
14 In their theoretical paper Irmen and Thisse (1998) show that when duopolists compete in multiple dimensions they will choose
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
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:
d=
u1 − u0 − p
τ
(2)
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:
p = u1 − u0 −
τg
2
(3)
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
(4)
2
The monopoly will choose the geographic extent that maximizes profit, which I will refer to as L∗ :
g∗ =
u1 − u0 − c
≡ L∗
τ
(5)
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 215 . 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
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∗
15 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
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
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:
F
τg = Dc +
AR(g) = AC(g) : D u1 − u0 −
2
g
F
D =
g u1 − u0 − c − τg
2
(6)
(7)
Equation 7 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
make the monopolist’s profit equal to zero for geographic extent L∗ /216 . 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
(8)
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 7
and substituting NL for D I can write the expression giving the minimum population required for entry as a
function of land:
2N ∗ L∗ L
Nmin (L) =
(9)
g(2L∗ − g)
16 Average
F
cost is plotted on the $/D scale and thus the curve plotted is average cost divided by density: c + Dg
.
8
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∗
(10)
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 firms17 . 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.
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
B
NminHL; n=1,∆=.5L
N .2
N *.5
*
L* 4L*3
No entry
2L*
5L*2
3L*
Land Area
(a) Multiple Firms
2.2
A
*
L*2
L*
3L*2
2L*
Land Area
(b) Multiple Types
Population, Land, and Variety
To investigate variety I will assume that consumers have heterogeneous tastes and will only consume their
preferred variety. There are V different varieties in the market and the distribution of varieties can be repreV
sented by the vector δ = {δ1 , δ2 , ..., δV }. Consumer have a taste for only one variety so that
∑ δi = 1. I will
i=1
further assume that consumers are located uniformly throughout the perimeter of the circle so that if I were
to randomly select any segment the percentage of consumers favoring cuisine v is always equal to δv , the
17 With
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.
9
percentage of that taste in the population18 . Firms of type v only compete for the total number of customers
of type v, equal to N ∗ δv . All firms, regardless of type, have the same fixed cost F and marginal cost c and
thus have the same minimum population for each value of land. If the market has N 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”
(11)
Nmin (L; δv ) =

 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
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)
=
(12)

∂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
#Varietiesm ∼ Im = Nm 1 − ∗ 1(Lm ≤ L∗ ) +
1(L∗ < Lm )
(13)
2L
2Lm
18 An
alternative and equivalent assumption would be to assume all consumers are identical and consume δv amount of each
cuisine. Note that this alternative assumption could be considered one form of a ”taste for variety.” If one city offers more variety
than another then the representative consumer will consume more restaurant meals in the more diverse city.
10
Specifically (and dropping subscripts):
L∗
∂ #Varieties
L
∼
1 − ∗ 1(L ≤ L∗ ) + 1(L∗ < L) > 0
∂N
2L
2L
∗
∂ #Varieties
−N
−NL
∗
∼
1(L
≤
L
)
+
1(L∗ < L) < 0
∗
2
∂L
2L
2L
(14)
(15)
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. 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
Describing City Product Variety
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 cities19 . 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.
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. I
19 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
therefore ended up collecting many Census places within the vicinity of large cities (in estimation I will use
MSA fixed effects when appropriate). 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 Cen#CitySearchRestaurants
and keep all Census places with a match ratio between
sus place as MatchRatio = #EconomicCensusRestaurants
20
.7 and 1.1, leaving 726 Census Places .
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$. Overall, about 40% of the restaurants have price
data and in defining cuisine measure 2 (m2) I break up each cuisine into 5 subgroups: one subgroup for each
of the four price levels and another if the price is missing. Given the fill rate and coarseness of these prices
I will concentrate mainly on the m1 measure and use the m2 measure as additional evidence. In Table 12
(Appendix) I list all the cuisines and the count of cities in each land quartile with that cuisine. The rarest m1
cuisines are Armenian and Austrian, found in just two cities21 while there are a number of cuisines found in
every or nearly every city (Chinese, Deli, Fast Food, Italian, Mexican, Pizza). The rarest m2 cuisines do not
always correspond to m1; for example “Caribbean” restaurants are found in 96 cities but only 3 cities have
a 4$ 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 in the left panel represent the number of cuisines (measure
1) plotted against the number of restaurants for all 726 Census Places, where both axes are in logs. As the
number of restaurants increases the number of cuisines first rises rapidly and then becomes roughly linear (in
logs). The number of cuisines rises far more slowly with the number of restaurants than would be predicted
from simply randomly assigning cuisines to restaurants with equal probability over all cuisines (results from
uniform multinomial simulations available upon request and in earlier versions). However, one might also
wonder how this pattern compares to randomly assigning cuisines to restaurants based on the observed
nationwide distribution of restaurants to cuisines. A theory underlying this type of null distribution could be
that the cuisine of a restaurant is determined entirely by the cuisine-specific skills of the restaurateur and the
20 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.
21 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
12.9
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
18.9
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]
13.7
[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
25.7
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
52.2
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]
41.2
[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%]
restaurateurs in every city are drawn from a nationwide distribution across skills. If some skills are relatively
rare and others are quite common then cities with many restaurants are more likely to have a rare cuisine and
cities with few restaurants will have just common cuisines22 . An implication of this skill-set hypothesis is
that every restaurant exists in its own independent market, unaffected by city level characteristics. Therefore
aggregating a city’s n restaurants and looking at features of the cuisines should be no different from randomly
drawing n restaurants from many different cities. Thus to compare to this hypothesis I draw restaurants for
each city from the nationwide pool with replacement and then for each city show the 1st and 99th of the
number of cuisines from 1000 simulations23 . This means that confidence bands shown in the left-hand
panel of Figure 4 for each city do not come from the same replication (simulation run) but rather represent
the city-specific bands, across all runs (similar to looking at a distribution of maxima). The figure shows
that for many cities the observed number of cuisines is significantly below even the 1st percentile of the
simulations. To look at the likelihood of finding so few cuisines across many cities in the same replication
I run locally weighted regressions (lowess) of log cuisines against log restaurants for each replication and
then show the 1st and 99th percentile bands from the predicted values. I compare this to the predicted values
from a lowess regression on the observed data24 . The confidence bands are quite narrow and the observed
22 In this paper I wish to show features of the observed distribution and then suggest a model that would generate this distribution.
If the observed distribution across cities is not exogenous but rather generated by features of cities, as suggested in my model,
then testing against the empirical distribution can be problematic. As an example from a different context, 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 (Baumgardiner (1988)
suggests specialization is endogenous to local market conditions). If we took the empirical distribution of doctors to specialties
and then randomly assigned doctors to specialties from this distribution then large cities, which have more doctors, would have
more specialized doctors. However, this type of test could falsely reject the theory since the theory suggests a distribution and the
test would be effectively assuming that distribution. Nonetheless, in the case of restaurants the observed distribution of cuisines
across cities is even quite different from the empirical distribution of restaurants across cuisines and so I use this comparison
distribution for robustness.
23 Results from simulations without replacement are even further from the observed data.
24 While the percentile bands for two cities could still come from different replications the predicted values for any city are
affected by all the other cities in that run and thus this technique is an approximation to looking at the whole cuisine-restaurant
distribtion across many replications.
13
data is significantly below the 1st percentile for every city except the very largest cities, of which there are
few. Therefore, even in comparison to the skill-set theory the number of cuisines rises more slowly with the
number of restaurants, consistent with a threshold model.
Figure 4: Number of Cuisines vs Number of Restaurants
Lowess Plot of Log M1 Cuis~Log Restaurants
with CI from Empirical Distribution (w replacement)
Number cuisines, log scale
20
40 6080
Number cuisines, log scale
20
40 6080
100
Number M1 Cuisines against Number Restaurants
with CI from Empirical Distribution (w replacement)
5
10 15
5
Number of restaurants, 000’s, log scale
number m1 cuisines
1st to 99th pctile band (simulation)
The CI were calculated by drawing the number of restaurants for each city from the empirical
distribution with replacement. I then take the 1st and 99 percentiles of the number of cuisines,
drawing separately for each city.
10 15
Number of restaurants, 000’s, log scale
1st, 99th pctile (sim)
predicted # m1 cuisines (data)
The CI were calculated by drawing the number of restaurants for each city from the empirical
distribution with replacement. I then run a lowess regression for each of the 1000 simulations
and plot the 1st and 99 percentile range of lowess predicted values
(a) Percentile Bands
(b) Lowess Plot
In addition to the count of cuisines across cities, there is also a systematic, hierarchical pattern to the
specific cuisines found in each city and the number of restaurants. Mori, Nishikimi, and Smith (2008)
investigate the distribution of industries across Japanese cities and find a strong hierarchical pattern that
results in several empirical regularities. Hsu (2012) finds a similar pattern in US data and proposes a model of
Central Place Theory consistent with these regularities. In Hsu’s model (2012) scale economies in production
lead to a central place hierachy but he also notes that heterogeneity in demand would lead to the same
hierarchical structure of goods across cities. While in this paper I focus on non-tradable consumer products
and also incorporate spatial concentration in addition to population size, the underlying mechanism of my
model–demand aggregation–is consistent with Hsu’s model. I therefore use several of the techniques from
MNS (2008) to describe the pattern of cuisines across cities and show that this pattern is quite similar to the
Central Place patterns found in the distribution of industries across cities.
In Figure 5 I show hierarchy diagrams from MNS for each cuisine measure. For each cuisine I count the
number of cities that have that cuisine, “choice cities,” and for each city I count the number of cuisines in the
city. 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)25 . Each observation is a city-cuisine pair and it can immediately be seen that cities
with more cuisines also have the rarer cuisines. Further, if a city has a rare cuisine that city also tends to have
all of the more common cuisines. This implies that simply knowing the count of cuisines allows prediction
of the specific cuisines found in the city.
25 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
cuisine rank (ascending by count of choice cities)
0
100
200
300
400
cuisine rank (ascending by count of choice cities)
0
20
40
60
80
100
Figure 5: 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
MNS propose a hierarchy statistic that captures this pattern and then compare the statistic to draws from
a uniform multinomial. When I do this (see Appendix) I find that the pattern of cuisines across cities is far
more hierarchical for both cuisine measures than that from a uniform distribution across cuisines. However,
their test implies that comparison distributions must be at the cuisine level, meaning that in simulations for
each city I draw n cuisines, rather than n restaurants and then determine the number of cuisines26 . In order
to compare the hierarchical pattern in the data to simulations from the empirical distribution of restaurants
(skill-set hypothesis) I use a closely related technique from the same paper, the Number Average Size plot.
For each cuisine I calculate the average number of restaurants found in the corresponding choice cities.
In the left-hand panel of Figure 6 I plot the 90 m1 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 linear in logs relationship with
an elasticity of −.55 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. On the right I plot
the 359 m2 cuisines and also find a linear in logs relationship (elasticity −.38) 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.
I compare this to the 1st and 99th percentiles from simulations in which I draw from the empirical
distribution of restaurants with replacement, as done in the earlier exercise. Again, the bands are calculated
at the cuisine level and thus represent the percentiles across all simulations for each cuisine. The plots
shows that the average number of restaurants in the choice cities of each cuisine is often higher than the 99th
percentile from the simulations, indicating that rare cuisines are found in fewer and larger cities than would
26 The
problem with drawing at the restaurant level is that even for strongly hierarchical distributions, cities with many restaurants will receive many cuisines. This leads to many cuisines being found in every city, which differs from the observed pattern,
but still results in a high hierarchy statistic.
15
be predicted. While the simulation results are also linear in logs, that pattern is not nearly as steep with both
the intercept and the elasticity from the observed data greater than the 99th percentile of the simulations.
This shows that the skill-set hypothesis would not result in such a strong hierarchical pattern across cities.
Figure 6: Number Average Size Plots: Average Number of Restaurants in Cities with a Given Cuisine
NAS Plot for Cuisine M2
mean # restaurants, 000’s, log scale
5 1015
mean # restaurants, 000’s, log scale
5 1015
NAS Plot for Cuisine M1
200
400 600800
200
# choice cities, log scale
average # restaurants
400 600800
# choice cities, log scale
1st to 99th pctile band (simulation)
The CI were calculated by first drawing over the number of restaurants for each city from the empirical
distribution with replacement. I then calculate average number of restaurants in each cuisine and take
the 1st and 99 percentiles of these averages. I plot each cuisine against the number of choice cities from
the data. When multiple cuisines have the same number of choice cities I take the average. The slope
(elasticity) is −.55 and the intercept is 9.04, both greater in magnitude than 99th percentile of simulation.
average # restaurants
1st to 99th pctile band (simulation)
The CI were calculated by first drawing over the number of restaurants for each city from the empirical
distribution with replacement. I then calculate average number of restaurants in each cuisine and take
the 1st and 99 percentiles of these averages. I plot each cuisine against the number of choice cities from
the data. When multiple cuisines have the same number of choice cities I take the average. The slope
(elasticity) is −.38 and the intercept is 8.4, both greater in magnitude than 99th percentile of simulation.
(a) Cuisine Measure 1
(b) Cuisine Measure 2
Lastly, 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
Cmv =
(16)
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
ηv ’s, to be negative. Further the ratio γγ1v
represents the αv parameter27 , which gives the number of additional
people required for a city to have a cuisine, along the frontier, if the land area is increased by one unit. The
N∗
v
ratio −η
γ1v gives the population intercept for each cuisine ( δv )—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 model28 . I estimate each cuisine
27 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).
28 I also estimated the model with a probit and found similar results but with a slightly lower log likelihood for most cuisines.
16
separately and exclude cuisines when the estimated model fails a likelihood ratio test at the 5% level29 . 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% level30 . 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 intercept31 .
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.
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
The results from this section follow 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. There is a strong hierarchical pattern to the distribution of cuisines across cities that is statistically
different from the distribution of cuisines across restaurants. This pattern is consistent with the proposed
model of entry thresholds and quite similar to the Central Place Theory regularities found in the distribution
of industries across cities from other papers.
29 The
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).
30 I used the ”nlcom” package of Stata which uses the delta method to compute standard errors for the ratio of coefficients.
31 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.
17
3.3
Restaurant Ecology: Alternative Measures of Diversity
The simple model presented in this paper does not allow cross-cuisine competition and therefore its implications are unlikely to be useful in predicting the specific number of restaurants in each cuisine in each
city. However, as a descriptive exercise it’s informative to examine how demand aggregation affects general
distributional measures of restaurants across cuisines. For example, is the share of restaurants in each cuisine more even in larger cities? These distributional measures of diversity have been considered at length
in the ecology literature in the context of species diversity. Jost (2006) points out that many of the different
measures of diversity in ecology (and in economics) follow a common form:
S
q
D=
∑
i=1
!
q
pi
1
1−q
S
!
and when q = 1: 1 D = exp − ∑ pi ln(pi )
(17)
i=1
In this notation S is the count of species (cuisines), pi is the share of the total organisms in species i (restaurants in cuisine i), and the q is denoted the “order of diversity.” When q = 0 the function reduces to the
simple count of species. When q = 1 the function is defined by its limit and is equal to the exponential of
the Shannon entropy, which I will refer to as ”Shannon diversity.” When q = 2 the diversity measure is equal
to the inverse of the Simpson concentration, or the inverse of the Hirfindahl Hirschmman Index (HHI) of
market concentration in economics. Jost notes that as the order of diversity increases the weight on the least
common species decreases, with equal weighting of rare and common species at q = 1.
Without cross-cuisine competition my model implies that the share of restaurants in each cuisine should
not be affected by population and land area except through the entry/exit of cuisines32 . This is because the
share of total restaurants in a cuisine is always proportional to the percentage of the population with that taste.
Therefore as population and land area change the model would predict that the only effect on higher order
diversity measures (q > 0) would come through changing the number of cuisines. I can look directly at the
distribution of the share of restaurants in each cuisine by calculating measures of “evenness.” These measures
are used to evaluate the relative frequencies of different species in an environment (Olszewski 2004). I
calculate cuisine evenness as a given diversity index divided by the count of cuisines, which constrains the
measure between 0 (least even) and 1 (most even).
In Figure 8 I plot three measure of diversity (q = 0, 1, 2) and their corresponding evenness indices against
log population, using the two different cuisine measures. For clarity I have plotted the smoothed estimates
from a locally weighted regression of each measure against log population. Looking at the diversity measures, the number of cuisines rises rapidly while the Shannon and Simpson diversities rise slowly. Further,
the evenness measures decline monotonically in city population, indicating that bigger cities have a far less
even distribution across cuisines. In theory this does not have to be the case: if ethnicity was the main factor driving cuisine diversity and bigger cities had a more even distribution across ethnicities then we might
expect to see the number of cuisines and evenness increasing with population. Empirically however, larger
cities have more cuisines but there are fewer restaurants in these additional cuisines, which decreases the
evenness. These plots are consistent with the model in that the greater restaurant diversity of larger cities
occurs through the addition of rarer cuisines.
32 This
is not precisely correct because changing population or land area could change the equilibrium for a subset of the
cuisines in a city. The equilibrium for each cuisine determines the number of firms and depends upon the density of consumers
(see discussion of multiple firms in Appendix). It’s possible that in the same city firms selling a rare cuisine, small δ , face a low
enough density of consumers to be in the monopoly equilibrium while firms selling a more common cuisine are in the competitive
equilibrium. Changing the population or land area could switch the equilibrium for these cuisines, and thus their relative shares
of restaurants, without entry or exit of a new cuisine. I consider this a technical point that is not empirically testable with my data.
18
.8
Evenness measures
200
1
80
Figure 8: Distributional Measures of Cuisine Diversity
8
10
12
Population 07-08 (logs)
Number Cuisines (m1)
Simpson Diversity (m1)
Simpson Evenness (m1)
14
16
.8
.4
.6
Evenness
8
Shannon Diversity (m1)
Shannon Evenness (m1)
10
12
Population 07-08 (logs)
Number Cuisines (m2)
Simpson Diversity (m2)
Simpson Evenness (m2)
(a) Cuisine Measure 1
4
.2
0
Diversity measures
0
0
0
.2
Diversity measures
50
20
Diversity
40
.4
.6
Evenness
Diversity
100
150
60
Evenness measures
14
16
Shannon Diversity (m2)
Shannon Evenness (m2)
(b) Cuisine Measure 2
Empirics
4.1
City level estimation
The model in the theory section showed how demand aggregation affects variety when cities are identical in
characteristics. To incorporate differences in the characteristics of cities I assume the population of a market
S
Nm can be completely partitioned into a set of groups S: Nm =
∑ Nms.
These groups could be defined by
s=1
demographic characteristics, such as ethnicity, income, or education, and group specific affinities for cuisines
implies their relative size could affect a city’s variety:
! S
Lm
L∗
Nms
∗
∗
1 − ∗ 1(Lm ≤ L ) +
1(L < Lm )
(18)
#Varietiesm ∼ Nm ∑
2L
2Lm
s=1 Nm
To estimate the above equation I take logs and replacing the log of the percentage sub-groups ( NNms
) with the
m
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 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 area33 . These
simplifications lead to a straight-forward log linear specification:
ln(#Cuisinesm ) = γ0 + γ1 ln(Nm ) + γ2 ln(Lm ) + Xm 0β + εm
(19)
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.
33 The
19
In equation 19 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. In
addition, I include 45 ethnicity control variables, calculated as the percentage of the city’s population born
in a given country (ex: percentage Argentine) from the 2000 US Census. 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. In order to allow for the possibility that residents of a given city travel to other cities
within the same Metropolitan Statistical Area (MSA) I include MSA fixed effects and cluster at the MSA
level. 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 (measure 1) and a 5% increase in the count
of cuisine-price pairs (measure 2). I also find that 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 coefficient
on population roughly increases with each land quartile. Further, the coefficient on land area declines over
the quartiles until reaching the last quartile where it becomes negative and statistically significant for both
cuisine measures. The magnitude of these coefficients is fairly large, indicating that a 10% decrease in land
area, which effectively increases density without changing population, increases the number of cuisines by
2.2% and 2%.
I also look at the diversity within a cuisine and find similar results. I define within cuisine diversity as
the number of price-cuisine pairs, or subcuisines, within any given cuisine; the number of subcuisines can
range from 1 to 5. I then estimate the following specification:
#SubCuisinesmv = γ0 + γ1 ln(Nm ) + γ2 ln(Lm ) + γ3 ethmv + Xm 0β + εmv
(20)
The unit of observation is the city-cuisine pair (mv) and for any given cuisine I only include cities with at
least one restaurant in the cuisine (no zeros), and cluster at the city level. This makes the specification similar
to running a regression on the number of subcuisines, demeaned at the cuisine level, and then aggregated
back up to the city level. However, in two of the specifications I also include the ethnic percentage of the
city corresponding to the cuisine, which varies at the city-cuisine level. For these specifications I can only
estimate across ethnic cuisines, which reduces the sample.
I present the results in Table 3 with and without MSA fixed effects. Focusing on column 2, which is run
for all cuisines, population increases the number of subcuisines; a 10% increase in population leads to about
a .042 increase in the number of subcuisines within any cuisine. This is about 8% of the standard deviation
of the number of subcuisines within the average cuisine. Land area has the expected negative effect and
again is much smaller in magnitude than the coefficient on population. When restricting the sample to ethnic
cuisines I find larger results on both population and land area. An interpretation of these results is that bigger,
denser cities are associated with greater within cuisine diversity for all cuisines and with a stronger effect for
ethnic cuisines.
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
20
Table 2: Number of Cuisines: Measure 1 and Measure 2
(a) Cuisine Measure 1
(1)
All
0.399***
(0.034)
(2)
All fe
0.397***
(0.038)
(3)
LQ4
0.220**
(0.098)
(4)
LQ3
0.383***
(0.088)
(5)
LQ2
0.495***
(0.118)
(6)
LQ1
0.511***
(0.045)
0.010
(0.033)
0.019
(0.039)
0.206
(0.137)
-0.066
(0.161)
-0.041
(0.174)
-0.229***
(0.056)
-0.593***
(0.098)
-0.586***
(0.105)
-0.946***
(0.280)
-0.523
(0.316)
-0.102
(0.279)
-0.648*
(0.338)
Med. HH Income (000’s)
0.004*
(0.002)
0.002
(0.002)
0.011
(0.007)
-0.005
(0.006)
-0.007
(0.009)
-0.000
(0.008)
%Old (> 64)
-0.184
(0.635)
-0.384
(0.791)
-0.556
(1.679)
-0.671
(1.463)
-0.681
(1.533)
-1.750
(2.095)
%Young (< 35)
0.144
(0.510)
-0.433
(0.503)
0.766
(1.173)
-1.576
(1.179)
-1.691
(1.119)
-1.228
(1.355)
%College grad
0.565**
(0.230)
703
0.818
NO
0.726***
(0.249)
703
0.854
YES
0.221
(0.844)
177
0.853
YES
1.540**
(0.750)
172
0.922
YES
1.068
(0.745)
175
0.894
YES
0.860
(0.690)
179
0.948
YES
Pop 2007-8 (logs)
Land sq mtrs (logs)
Average HH Size
Observations
R2
MSA FE
(b) Cuisine Measure 2
(1)
All
0.521***
(0.033)
(2)
All fe
0.525***
(0.036)
(3)
LQ4
0.336***
(0.112)
(4)
LQ3
0.461***
(0.118)
(5)
LQ2
0.605***
(0.136)
(6)
LQ1
0.626***
(0.053)
0.018
(0.032)
0.020
(0.038)
0.226*
(0.132)
-0.092
(0.191)
-0.093
(0.241)
-0.200***
(0.073)
-0.769***
(0.117)
-0.761***
(0.123)
-1.040***
(0.274)
-0.727*
(0.415)
-0.340
(0.342)
-0.645*
(0.379)
Med. HH Income (000’s)
0.006**
(0.003)
0.003
(0.003)
0.013*
(0.007)
-0.004
(0.007)
-0.006
(0.012)
-0.007
(0.009)
%Old (> 64)
-0.658
(0.782)
-0.726
(1.016)
-1.277
(1.782)
-1.304
(1.411)
-1.294
(2.006)
-2.414
(2.749)
%Young (< 35)
0.232
(0.604)
-0.428
(0.628)
0.624
(1.465)
-1.988
(1.210)
-1.002
(1.327)
-1.984
(1.945)
0.567**
0.698***
0.195
1.299
1.131
(0.252)
(0.263)
(0.865)
(0.873)
(0.917)
Observations
703
703
177
172
175
R2
0.853
0.883
0.871
0.928
0.892
MSA FE
NO
YES
YES
YES
YES
Standard errors in parentheses, clustered at MSA level. * p<0.1 ** p<0.05 *** p<0.01
Each regression is run with 45 ethnicity control variables which match cuisine varieties.
Note: 23 Census Places are not in MSAs and were dropped from estimation.
1.404*
(0.739)
179
0.954
YES
Pop 2007-8 (logs)
Land sq mtrs (logs)
Average HH Size
%College grad
21
Table 3: Diversity Within Cuisines: Number Subcuisines
(1)
(2)
(3)
(4)
All
All FE
Ethnic
Ethnic FE
Pop 2007-8 (logs)
0.422*** 0.423*** 0.550***
0.541***
(0.037)
(0.038)
(0.051)
(0.051)
Land sq mtrs (logs)
-0.086***
(0.029)
-0.070**
(0.032)
-0.158***
(0.040)
-0.120***
(0.042)
Average HH Size
-0.359***
(0.059)
-0.397***
(0.069)
-0.432***
(0.085)
-0.454***
(0.099)
0.000
(0.002)
-0.000
(0.002)
0.000
(0.002)
-0.001
(0.003)
-1.031**
(0.491)
-0.934*
(0.493)
-1.516**
(0.683)
-1.258*
(0.681)
%Young (< 35)
-0.421
(0.422)
-0.616
(0.459)
-0.767
(0.597)
-0.996
(0.646)
%College grad
0.415***
(0.142)
0.412***
(0.155)
0.756***
(0.224)
0.822***
(0.233)
12967
0.435
YES
0.098
(0.183)
5790
0.452
NO
0.185
(0.182)
5713
0.480
YES
Med. HH Income (000’s)
%Old (> 64)
Corresponding ethnic %
Observations
R2
MSA FE
13168
0.418
NO
A subcuisine is a cuisine-price pair within a cuisine, such as Indian price 2.
Standard errors in parentheses, clustered at Census Place level. * p<0.1 ** p<0.05 *** p<0.01
Unit of observation is cuisine-city pair. All specifications include cuisine fixed effects.
22
indicator I write:
Cmv =


1
if Nm


0
o/w
S
Nms
∑ Nm
s=1
!
h
1−
Lm
2L∗
L∗
1(L∗
1(Lm ≤ L∗ ) + 2L
m
i
< Lm ) ≥ N ∗
(21)
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
(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 markets34 . 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 and estimate the following
log-linearized specification:
Pr(Cmv = 1) = Pr(Π∗mv > 0)
Π∗mv = γ1 ln(Nm ) + γ2 ln(Lm ) + Xm 0β + 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 the top panel of Table 4 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 bottom panel
includes ethnicity controls 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 11. Generally the coefficients reflect the signs from the pooled specification in Table
4 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 5 I show classification results for the full model versus a logit model with
S
34 In the quadratic case variety v is found in market m if N
m
L∗ =
q
4
3τ (u1 − u0 − c)
Nms
∑ Nm
s=1
!
i
h
2
Lm
3L∗
∗
∗
∗
1 − 3L
∗2 1(Lm ≤ L ) + 2Lm 1(L < Lm ) ≥ N , where
and N ∗ , which by definition does not depend upon transportation cost, is the same (N ∗ =
23
F
u1 −u0 −c ).
Table 4: Likelihood of Having a Given Cuisine
(a) All Cuisines
(1)
All
0.101***
(0.003)
(2)
LQ4
0.087***
(0.010)
(3)
LQ3
0.113***
(0.008)
(4)
LQ2
0.140***
(0.008)
(5)
LQ1
0.139***
(0.006)
Land sq mtrs (logs)
-0.019***
(0.003)
0.022*
(0.013)
-0.011
(0.026)
-0.018
(0.023)
-0.045***
(0.007)
Average HH Size
-0.057***
(0.011)
-0.055***
(0.021)
-0.042**
(0.021)
-0.075***
(0.026)
-0.097***
(0.033)
Med. HH Income (000’s)
0.000
(0.000)
-0.000
(0.001)
0.000
(0.001)
-0.000
(0.001)
-0.001
(0.001)
%Old (> 64)
-0.052
(0.091)
0.033
(0.179)
0.047
(0.188)
-0.018
(0.218)
-0.327
(0.284)
%Young (< 35)
-0.071
(0.072)
0.084
(0.177)
-0.178
(0.137)
-0.049
(0.187)
-0.128
(0.177)
%College grad
0.164***
(0.026)
65340
.59
90
0.207***
(0.052)
11946
.45
66
0.178***
(0.054)
12558
.52
69
0.251***
(0.064)
12670
.55
70
0.253***
(0.073)
16380
.63
90
Pop 2007-8 (logs)
Observations
Pseudo R-squared
Number of cuisines
(b) Ethnic Cuisines Only
(1)
All
0.082***
(0.003)
(2)
LQ4
0.084***
(0.009)
(3)
LQ3
0.101***
(0.007)
(4)
LQ2
0.123***
(0.008)
(5)
LQ1
0.122***
(0.005)
Land sq mtrs (logs)
-0.021***
(0.003)
0.016
(0.013)
-0.031
(0.021)
-0.013
(0.023)
-0.038***
(0.007)
Average HH Size
-0.040***
(0.009)
-0.047**
(0.020)
-0.029*
(0.017)
-0.059**
(0.026)
-0.077***
(0.029)
Med. HH Income (000’s)
-0.000
(0.000)
-0.000
(0.001)
-0.000
(0.000)
-0.000
(0.001)
-0.001
(0.001)
%Old (> 64)
0.017
(0.072)
0.028
(0.145)
0.064
(0.158)
0.135
(0.210)
-0.021
(0.264)
%Young (< 35)
-0.038
(0.055)
0.048
(0.142)
-0.109
(0.108)
0.040
(0.173)
-0.024
(0.171)
%College grad
0.165***
(0.021)
0.189***
(0.053)
0.174***
(0.045)
0.268***
(0.063)
0.277***
(0.066)
Pop 2007-8 (logs)
%Corresponding ethnicity
0.192*** 0.205*** 0.234*** 0.233***
0.394***
(0.020)
(0.046)
(0.045)
(0.044)
(0.082)
Observations
42834
6697
7462
7240
10738
Pseudo R-squared
.62
.48
.55
.58
.65
Number Cuisines
59
37
41
40
59
Dependent variable is cuisine-city indicator, marginal effects of coefficients shown.
All specifications run with cuisine fixed effects.24
Standard errors in parentheses, clustered at Census Place level. * p<0.1 ** p<0.05 *** p<0.01
Table 5: Full Model Classification Table
Predicted
0
Actual
1
Cons Only
Full
Cons Only
Full
0
46,136
47,095
5,410
3,161
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
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%).
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
comparison35 . 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 ethnicity36 . 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 6 and by cuisine in Table 7, 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 7 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,
35 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.
36 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.
25
Table 6: 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.
and thus decreasing land area should not increase their likelihood of having those cuisines. It may also be
that for cities of that size transportation costs are already quite low. 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 4.
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 6 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 becomes 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.
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 reverse causality:
perhaps restaurant diversity, or another factor correlated with restaurant diversity, actually increases population concentration (the “endogenous quantity of labor” problem in CDG). A different way of viewing
this problem is that conditional on population size, some of the factors that increase density may also affect
restaurant diversity. For example, a city with pro-density zoning laws and land use constraints may also have
a culture favorable to restaurant diversity.
To address this problem, I use several variables that can predict smaller land areas conditional on current population—predict greater density—but that may not be associated with present-day factors affecting
restaurant diversity. For the first instrument I follow Abel, Dey, and Gabe (2012) who used the population
26
Table 7: 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
27
of the city’s county in the year 1900 as an instrument for current log density (their specification does not
include population and land separately)37 . While the authors justified this instrument under the assumption
that there is a persistence in population that is unrelated to current productivity, I am instrumenting for land
area conditional on population under the assumption that the persistence in population results in cities with
exogenously higher density today. The argument is thus slightly different: cities in areas with historically
larger populations would have developed in an era of earlier transportation technology and thus be denser
today due to a persistence in city layout and structure. As an additional instrument I include the share of unavailable land in the principal city of each MSA from Saiz (2010)38 . The share of unavailable land is based
exclusively on measures of geography (presence of water bodies, slope of land) and thus cities in areas with
less developable land may be naturally constrained to higher densities.
I estimate the earlier specification from Table 2 using these instruments and show the results in Table
8. The variation in my instruments is mostly at the MSA level and so I do not include MSA fixed effects
but do cluster at this level. I also do not have enough variation to include the earlier 45 ethnicity control
variables so I instead proxy for ethnic diversity with ethnic HHI, calculated as the sum of squared ethnicity
shares. The first column of Table 8 re-estimates the OLS specification across all quartiles with these variable
changes and is fairly similar to earlier. In column 2 I instrument for land area with the county population in
1900 and find a similar effect of population and again no effect of land area. In the remaining four columns I
focus just on the largest land quartile where I had found land area had a significant negative effect in earlier
estimates. Comparing the OLS estimate of this quartile (column 3) to the historic population IV estimate
I find larger coefficients on population and land area but with a significantly larger standard error on land
area. Further, comparing the Kleibergen-Paap statistic (for clustered errors) to the Stock and Yogo critical
values suggests the instrument is weak. I therefore include the p-value from the Anderson Rubin test, which
has correct size in the presence of weak instruments, and reject that the coefficient on log land area is zero
for this and all IV specifications. In column 5 I instrument with the share of unavailable land, which is a
stronger instrument, and leads to even larger coefficients on population and land area. In specification 6 I
use both instruments and find a coefficient between the two earlier IV estimates. Clearly the results are quite
sensitive to the choice of instrument but all specifications show a large and significant negative effect of land
area. This provides further evidence that density–controlling for scale (population)–can have an important
effect on product variety.
An additional and separate endogeneity problem arises 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 dense 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
37 I
match Census Places to counties and obtained historical population data from the National Historical Geographic Information System (NHGIS 2011).
38 Saiz calculates his measure for principal cities of MSAs with gerater than 500,000 people and thus the data is at the PMSA,
MSA, or NECMA level. I first match Census Places to PMSAs and then for Census Places I cannot match directly to a PMSA I
assign the value of the PMSA for the shared MSA. For example, Anaheim, CA cannot be matched directly to a PMSA in the Saiz
data so I assign it the value of the Los Angeles PMSA since both Anaheim and Los Angeles are in the LA-Riverside MSA. For
this work the MableCORR system was very helpful (MableGeocorr 2010).
28
Table 8: Instrumented Specifications
(1)
OLS
0.403***
(0.036)
(2)
IV
0.433***
(0.093)
(3)
OLS LQ1
0.478***
(0.041)
(4)
IV LQ1
0.532***
(0.103)
(5)
IV LQ1
0.629***
(0.084)
(6)
IV LQ1
0.606***
(0.079)
0.006
(0.035)
-0.025
(0.095)
-0.179***
(0.038)
-0.266*
(0.154)
-0.434***
(0.127)
-0.384***
(0.112)
-0.492***
(0.095)
-0.484***
(0.100)
-0.430**
(0.200)
-0.394*
(0.202)
-0.458**
(0.198)
-0.335**
(0.169)
0.004*
(0.002)
0.004*
(0.002)
0.002
(0.004)
0.001
(0.004)
-0.000
(0.004)
-0.000
(0.004)
-0.886***
(0.113)
-0.822***
(0.231)
-0.278
(0.176)
-0.139
(0.282)
0.073
(0.287)
0.053
(0.252)
%Old (> 64)
0.128
(0.586)
0.081
(0.605)
0.004
(1.174)
-0.262
(1.201)
-2.384
(1.704)
-0.681
(1.400)
%Young (< 35)
0.187
(0.418)
0.145
(0.473)
0.819
(0.743)
0.629
(0.833)
-0.779
(1.022)
0.287
(0.948)
%College grad
0.616***
(0.207)
639
0.795
Pop 2007-8 (logs)
Land sq mtrs (logs)
Average HH Size
Med. HH Income (000’s)
Ethnic HHI
0.611***
0.812**
0.846**
0.467
0.920***
(0.202)
(0.337)
(0.329)
(0.464)
(0.318)
Observations
639
149
154
173
149
R2
0.794
0.860
0.856
0.791
0.830
Instrument(s)
1
1
2
1 and 2
Cragg Donald F Stat
53.13
8.51
14.84
11.19
K-P Wald F
29.01
6.96
12.26
14.66
Stock Yogo 10% Size
16.38
16.38
16.38
19.93
Stock Yogo 15% Size
8.96
8.96
8.96
11.59
Anderson Rubin p-val
0.786
0.035
0.000
0.000
Standard errors in parentheses, clustered at MSA level. * p<0.1 ** p<0.05 *** p<0.01
IV specifications instrument for log land area. Instrument 1 is county population in 1900, instrument 2
is share of unavailable land from Saiz QJE 2010. For specification 6
I test the overidentifying restrictions and find a Hansen J statistic p-value of .3092, indicating valid instruments.
29
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
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
∑ (Xi − X̄)
∑ wi j
N
N
∑
i=1 j=1
(22)
i=1
In equation 22 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 neighbors39 ; 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 analysis40 . 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 9 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 4, adding in the Moran’s I statistic and again,
restricting to the top land quartile. In the first column of panel of Table 10 I run the previous specification
on the reduced sample and obtain similar results to column 8 of Table 4. 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
39 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.
40 I used the ”spdep” package in R to run the analysis.
30
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 ethnic
cuisines, removing cuisines with too few observations to be estimated, and include controls, cuisine fixed
effects, and city fixed effects. The third column of Table 10 shows that census tracts with larger populations of ethnicity v are more likely to have a corresponding restaurant while the fourth column 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 coefficients41 . 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
In this paper I have argued that a significant amount of variety in the restaurant market results from the
aggregation of specific tastes from a heterogeneous population. I presented a simple model of demand
aggregation where the fixed cost of opening up a restaurant combined with heterogeneous tastes led to cuisine
specific entry thresholds. The importance of transportation cost in restaurant consumption implies that the
spatial distribution of a population is a key determinant of whether demand passes this threshold. 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. In the empirical
section I found that the pattern of cuisines across US cities follows a fairly regular hierarchical distribution
that is consistent with this type of threshold model and echoes findings from Central Place Theory papers
studying industrial composition. Varieties that appeal to fewer people are much more likely to be found
in bigger and denser cities because spatial aggregation becomes more important when demand is limited.
For this reason, larger and denser cities have both greater variety and rarer varieties of restaurants. This
finding was consistent across multiple specifications, including within cuisines and when estimated at the
cuisine-level, and when using instrumental variables to estimate the effect of density. 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 the effect
of demand aggregation on one of the important consumer benefits of agglomeration.
41 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.
31
Table 9: 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 32
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 10: Likelihood of having a given cuisine with clustered ethnic populations
Places (LQ1)
Tracts (All)
(1)
(2)
(3)
(4)
Logit
Logit
OLS
OLS
Pop 2007-8 (logs)
0.133***
0.120***
(0.006)
(0.006)
Land sq mtrs (logs)
-0.042***
(0.007)
-0.037***
(0.007)
Average HH Size
-0.082***
(0.032)
-0.080***
(0.031)
-0.028***
(0.003)
-0.027***
(0.003)
Median HH income (000’s)
-0.001
(0.001)
-0.001
(0.001)
-0.000**
(0.000)
-0.000**
(0.000)
%Old (> 64)
-0.070
(0.281)
-0.067
(0.282)
-0.025*
(0.015)
-0.023
(0.016)
%Young (< 35)
-0.047
(0.187)
-0.047
(0.186)
0.028***
(0.006)
0.035***
(0.006)
%College grad
0.303***
(0.072)
0.307***
(0.071)
0.034***
(0.006)
0.038***
(0.006)
%Corresponding ethnicity
0.428***
(0.089)
0.372***
(0.094)
Moran’s I
0.292***
(0.015)
0.136***
(0.022)
Corr. Ethic Pop (000’s)
0.024***
(0.002)
Remaining Pop (000’s)
0.002***
(0.000)
959753
0.236
Observations
r2
Pseudo R-squared
9790
9790
.63
.64
959753
0.237
Dependent variable is cuisine-place or cuisine-tract indicator, marginal effects shown for logit specifications.
All specifications run with cuisine fixed effects; tract-level specifications also have Census Place fixed effects.
Standard errors in parentheses, clustered at Census Place level. * p<0.1 ** p<0.05 *** p<0.01
33
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33(2), 221–242.
M AZZOLARI , F., AND D. N EUMARK (2010): “Immigration and product diversity,” Journal of Population
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Relationship between Industrial Location and City Size,” Journal of Regional Science, 48(1), 165–211.
M ORI , T., AND T. E. S MITH (2011): “AN INDUSTRIAL AGGLOMERATION APPROACH TO CENTRAL PLACE AND CITY SIZE REGULARITIES*,” Journal of Regional Science, 51(4), 694–731.
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35
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 =
(23)
dc
(24)
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
(25)
pk = u1 − u0 −
(26)
pm
(27)
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 extents42 .
 ∗ ∗ 2
N L n
∗

if L ≤ 2n
 L
3 L , ”full coverage, competitive equilibrium”





∗ L∗ n2
∗
∗
Nmin (n, L) = 2N
(28)
if 2n
2nL∗ −L
3 L < L ≤ nL , ”full coverage, kinked equilibrium”






 2N ∗ L
if nL∗ < L, ”partial coverage, local monopoly equilibrium”
L∗
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.
42 If
36
6.2
Hierarchy Test of Mori, Nishikimi, and Smith (2008)
Following MNS, I formally define a hierarchical structure of cuisines across cities as a distribution such that
if a cuisine is found in a cities with n cuisines it will also be found in all cities with greater than n cuisines.
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 5. 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 hypothesis. When I calculate the hierarchy share for all 726 places I find a hierarchy share of 23% for
cuisine measure 1 and 16% 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.
6.3
Additional Estimation Results and Statistics
Tables follow.
37
Table 11: 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]
38
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 12: 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
2
1
1
0
0
1
1
0
0
0
0
21
7
7
8
6
3
91
67
43
20
7
7
1
0
1
0
0
0
0
0
41
39
2
1
0
0
1
0
1
57
26
43
0
0
0
65
56
13
6
3
0
0
0
0
0
4
2
1
0
1
1
0
0
0
6
5
2
0
0
0
13
9
4
6
2
3
0
0
0
0
0
6
6
0
0
0
1
LQ3
2
0
1
1
0
2
1
1
0
0
0
45
7
32
7
7
4
128
108
70
34
9
7
1
0
1
0
0
0
0
0
63
59
6
0
0
0
0
0
0
83
48
61
5
1
0
121
106
36
12
3
0
0
0
0
0
1
0
1
0
0
0
1
1
0
31
24
5
5
1
1
19
9
5
8
2
3
1
0
0
0
1
14
11
3
1
0
0
LQ2
4
3
0
1
0
4
2
2
0
0
0
68
16
47
10
10
7
153
122
106
56
11
15
1
0
1
0
0
0
0
0
90
88
6
4
0
0
0
0
0
112
76
85
4
0
0
151
132
55
16
2
0
0
0
0
0
8
4
1
2
0
1
1
1
0
30
23
5
2
0
0
32
20
6
16
7
4
0
0
0
0
0
17
14
2
3
0
1
LQ1
CUISINE
9 Central European
6 MISS
21
22
23
20 4
16 Chilean
10 MISS
6 Chinese
5 MISS
11
119 2
39 3
103 4
38 Coffee Shops & Diners
28 MISS
22 1
173 2
165 3
150 Colombian
114 MISS
52 1
55 2
10 Cuban
3 MISS
51
52
43
14
2 Deli
2 MISS
128 1
126 2
30 3
17 Desserts
7 MISS
31
12
13
04
152 Dim Sum
132 MISS
130 1
19 Eastern European
9 MISS
11
170 2
160 3
115 4
57 Eclectic & International
6 MISS
71
32
43
24
2 Egyptian
21 MISS
51
92
5 English
9 MISS
61
22
23
14
81 Ethiopian
60 MISS
28 1
27 2
16 3
1 Filipino
70 MISS
40 1
36 2
52 French
19 MISS
81
42
23
14
1 German
0 MISS
59 1
49 2
17 3
16 4
7 Greek
2 MISS
1
2
3
4
LQ4
0
0
0
0
0
0
0
0
148
147
10
7
1
1
42
24
25
1
0
0
0
0
0
4
4
1
0
0
0
119
118
6
0
0
76
75
2
1
0
0
1
1
0
4
3
0
1
0
0
14
4
6
4
2
1
0
0
0
0
3
2
1
0
0
0
2
1
1
0
0
1
1
0
0
32
27
2
7
2
2
4
3
0
1
0
0
17
17
1
0
1
0
LQ3
0
0
0
0
0
0
0
0
169
169
19
6
3
1
72
42
49
0
0
0
0
0
0
2
0
1
0
0
1
147
145
10
1
0
107
105
6
4
0
0
0
0
0
4
4
0
0
0
0
21
9
13
5
4
2
0
0
0
0
5
2
2
2
0
0
1
1
0
0
0
1
1
0
0
52
43
4
10
8
4
6
6
0
0
0
0
43
42
3
2
0
0
LQ2
2
1
0
0
1
0
0
0
175
174
32
5
1
0
106
67
81
0
0
1
1
0
0
7
4
1
0
1
1
163
163
13
0
0
137
132
17
8
0
0
1
0
1
0
0
0
0
0
0
40
11
23
8
4
4
0
0
0
0
5
2
2
1
1
0
0
0
0
0
0
1
0
0
1
77
67
5
15
8
7
17
15
1
1
0
0
53
50
4
1
0
0
LQ1
CUISINE
5 Hamburgers
3 MISS
21
12
23
2 Health Food
3 MISS
31
178 2
178 4
75 Hot Dogs
36 MISS
10 1
42
153 Hungarian
128 MISS
127 1
12 Indian
4 MISS
91
82
13
24
30 Indonesian
18 MISS
14 1
11 2
33
0 Irish
171 MISS
171 1
46 2
83
2 Italian
162 MISS
161 1
47 2
26 3
54
4 Jamaican
2 MISS
21
02
13 Japanese
5 MISS
51
72
33
14
80 Korean
38 MISS
49 1
39 2
30 3
19 Kosher
3 MISS
11
12
14
24 Lebanese
13 MISS
14 1
72
24
1 Malaysian
11 MISS
71
62
23
1 Mediterranean
6 MISS
51
32
03
111 4
110 Meat‐and‐Three
22 MISS
42 1
32 3
31 Mexican
58 MISS
50 1
92
11 3
94
1 Middle Eastern
114 MISS
113 1
32 2
20 3
7 Moroccan
2 MISS
1
2
3
4
LQ4
LQ3
LQ2 LQ1
CUISINE
30
51
73 126 Noodle Shop
11
18
23
66 MISS
19
39
56 105 1
1
4
5
16 2
0
0
0
3 Latin American
3
5
6
54 MISS
1
1
2
20 1
2
3
4
43 2
0
1
0
33
0
0
0
14
3
8
12
32 Pizza
2
3
6
16 MISS
1
6
6
21 1
0
0
0
12
0
0
1
33
0
0
0
34
0
0
1
0 Polish & Czech
21
39
56 106 MISS
19
37
54 103 1
1
6
11
37 Polynesian
6
4
4
22 MISS
1
0
1
41
0
0
0
23
0
0
0
10 Portuguese
0
0
0
8 MISS
0
0
0
21
0
0
0
12
0
0
0
1 Puerto Rican
6
8
17
39 MISS
6
5
13
28 1
1
2
1
17 2
0
1
3
6 Russian
0
0
0
2 MISS
91
120
147 170 1
80
116
137 167 2
28
43
74 134 4
16
28
53 105 Scandinavian
4
11
18
46 MISS
3
4
3
24 2
0
1
0
6 Seafood
0
0
0
1 MISS
0
1
0
51
0
0
0
12
59
82
118 148 3
56
81
117 145 4
6
11
13
38 Soups
8
9
19
57 MISS
1
2
1
29 1
1
1
4
9 South American
10
15
21
62 MISS
10
15
20
60 1
0
1
2
10 2
0
2
2
83
0
0
0
24
3
0
3
15 Southern & Soul
3
0
3
14 MISS
0
0
0
31
0
0
0
22
0
0
0
13
1
2
2
18 4
1
1
1
6 Southwestern
0
1
1
10 MISS
0
0
0
31
0
0
0
12
0
3
3
83
0
2
2
44
0
0
1
3 Spanish
0
0
0
2 MISS
0
1
0
01
10
7
20
52 2
6
4
17
44 3
0
1
0
15 4
3
2
3
24 Steakhouse
1
2
1
15 MISS
1
0
2
61
0
0
0
42
0
0
0
23
0
0
0
34
0
0
0
1 Sushi
123
153
174 179 MISS
118
150
168 178 1
25
42
82 124 2
11
14
20
69 3
0
1
1
18 Swiss
0
0
0
3 MISS
8
16
21
70 2
8
12
18
57 Tapas / Small Plates
0
6
3
28 MISS
1
0
2
14 1
0
0
0
52
1
0
0
93
0
0
0
3
0
0
0
2
0
0
0
5
1
0
0
1
0
0
0
1
39
LQ4
5
5
1
0
3
2
1
0
0
0
164
154
63
1
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
54
12
12
8
4
27
27
0
1
1
0
0
0
0
4
4
0
0
0
0
3
2
1
0
0
0
2
1
0
1
0
0
35
24
1
2
9
6
6
3
0
4
0
0
0
0
2
1
0
1
0
LQ3
6
5
2
0
5
3
1
1
0
0
178
170
100
4
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
90
11
27
5
4
52
52
0
2
0
1
0
1
0
4
4
0
0
0
0
3
2
1
0
0
0
7
4
0
1
1
1
59
42
1
3
22
5
9
7
1
1
1
0
0
0
1
0
1
0
0
LQ2
7
5
2
1
5
1
3
1
2
0
178
176
138
9
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
101
30
40
9
8
74
74
0
2
2
0
0
0
0
8
5
2
2
0
0
6
5
1
0
0
0
12
9
0
3
0
0
79
53
0
3
31
5
11
8
2
2
1
0
0
0
5
3
0
2
0
LQ1
CUISINE
21 Thai
17 MISS
11 1
32
31 3
14 4
16 Tibetan
12 MISS
81
52
180 Turkish
180 MISS
165 1
31 2
23
1 Vegan
3 MISS
11
32
63
0 Vegetarian
4 MISS
31
32
33
04
1 Venezuelan
3 MISS
11
12
23
5 Vietnamese
4 MISS
11
32
13
24
0 Fast Food
2 MISS
161 1
139 2
88 4
104 Coffeehouse
42 MISS
33 1
107 2
107 3
2 Pan‐Asian & Pacific Rim
17 MISS
61
12 2
63
14
1 Family Fare
67 MISS
58 1
28 2
83
2 Cheesesteak
3 MISS
33 1
21 3
9 Chowder
9 MISS
41
12
37 3
30 4
8 Ice Cream
13 MISS
11 1
32
147 Bagels
126 MISS
11 1
22 2
93 Donuts
41 MISS
47 1
33 Juices & Smoothies
12 MISS
17 1
10
9
8
1
24
12
6
15
4
LQ4
LQ3
LQ2 LQ1
47
72
91 130
46
71
86 128
5
5
10
36
0
1
7
17
0
0
0
2
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
7
0
0
0
4
0
0
0
4
0
0
0
2
0
0
0
1
3
3
1
22
1
0
1
9
2
1
0
19
0
2
0
7
0
0
0
3
12
16
31
73
10
10
24
62
4
8
7
40
3
2
7
25
2
1
0
8
0
0
0
3
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
12
26
35
87
9
22
30
85
2
3
6
26
1
3
3
16
0
0
1
4
0
0
0
5
160
168
178 178
96
128
158 173
138
142
168 173
2
4
3
29
0
0
0
1
54
81
115 143
12
16
28
70
53
77
112 139
0
0
1
9
0
0
0
2
9
11
14
39
3
5
9
22
2
3
1
16
4
2
1
20
0
1
3
10
1
2
2
17
46
67
100 127
14
31
44
93
26
39
69 101
7
15
34
66
0
0
1
1
3
2
1
13
2
1
0
7
1
1
1
6
0
0
0
1
0
0
2
4
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
2
58
87
118 154
14
19
28
66
51
80
110 150
0
0
1
2
12
11
32
65
2
2
8
33
10
9
24
46
0
0
0
1
9
5
10
37
7
5
10
37
2
0
0
5
2
9
12
35
0
2
5
25
2
7
8
17