Urban sprawl and the planning efficiency frontiermiron/Miron2006USPEF.pdf · Urban sprawl and the...

Urban sprawl and the planning efficiency frontier

John R. Miron·

Professorof Geographyand City StudiesDepartment of Social Sciences

University of Toronto Scarborough1265Military Trail , Toronto , Canada M1C 1M

Phone4162877287Fax 4162877283

E-mail [email protected]://citieslab.utsc.utoronto.ca

Abstract

Urban development in Canada and America is driven by similar market forces and channeled by similar institutions.However, have evident differences in planning instruments made a difference in terms of the control of urban sprawlbetween the two nations today? This paper has three parts. In the first part, I present a conceptualization of the confl icting notions of urban sprawl. This leads to the idea of a planning efficiency frontier (PEF), a concept , which I useto characterize an efficient urban area from a perspective commonly ascribed to planners. We can then think of theshift of an urban area over time either toward or away from the PEF as an outcome of local political contestation. Inthe second part, I present two measures to assess sprawl. One is a measure of mean local density of population withinan urban area. The second is a measure of the variation in local density within an urban area. I argue that these twomeasures are important in characterizing the PEF. In the third part of the paper, I apply these measures using bettersupporting data, basically massive amounts of comparable geo-referenced small -area data from recent censuses, tocome up with a novel assessment of sprawl in urban areas in Canada (in 1996 and 2001) compared to America (in 1990and 2000). In the conclusion to the paper, I consider what that assessment tells us about the outcome of political contestation from one urban area to the next.

21 February 2006

Urban sprawl and the planning efficiency frontier Page 1

Urban development in Canada and America is driven by similar market forces and channeled by similar institu

tions . However, Canada differs from America in at least two respects. First, there has been no constitutional pro

tection for municipal government in Canada; municipalities are enabled by the provinces, and the provinces can

and do restructure them at will. This should mean that , down through history, provincial governments in Canada

have been better able than state governments in America to reorganize urban areas and their planning to deal

with sprawl at a metropolitan level. Second, because Canada does not guarantee property rights in its constitu

tion, planners there are thought to have had more leeway than do their American counterparts to control land use

and the spatial pattern of growth in urban areas. Consequently, planning regulation in Canada, particularly with

respect to zoning and land subdivision, was arguably stronger. At the same time, the American experience is dif

ferent because of federal legislation there -such as the Clean Air Act , Clean Water Act, Endangered Species Act,

and Intermodal Surface Transportation Efficiency Act-that has no equivalent in Canada. Such legislative develop

ments, which began in the 1960s and have been augmented down through the years, enable regulation of suburban

development at a regional scale, and can be used to tackle sprawl. Have such differences in planning instruments

made a difference on net? Are the effects comparable across the two nations? It is now almost two decades since

the Goldberg & Mercer (1986) comparison of Canadian and American cities: much has happened since then , and it

is fair to ask just how and why is urban sprawl different among urban areas in the two nations today.

However, before we can examine such a question, we have to be clear about the meaning of a term that is much

abused: urban sprawl. In the cacophony of discourses within the social sciences and city planning on the subject,

"urban sprawl" too often is an epithet hurled at a pattern or process that an author finds distasteful. 1 Like the

proud but apprehensive parent finding the gangling adolescent in soiled clothes draped over the family's new sofa,

the author might admire the vitality, but be overwhelmed by the physical changes that have occurred , the waning

of a more-innocent t ime, and a heightened sense of complexities and costs in today's world. It is similarly difficult

to maintain objectivity in the swirl of emotions in which we observe and critique urban sprawl ; caught as we are

between our disciplinary and professional lenseson the one hand and our aesthetic , social, and environmental sen

sibilities on the other. AsMyers and Kitsuse (1999, 2) argue:

We find all of the literature on this topic is very subjective, no matter how many objective facts are introduced into the debate ... As we will show, one man's sprawl is another one's compact development ... At root,evaluations of development density patterns and presumptions of desirable changes appear to be heavily flavored by preconceptions and unstated values. There can be little hope of progress toward resolving the impasse reached in this debate until these preconceptions have been brought to the surface.

Even worse, some authors equate the term with a specific urban area, often Los Angeles.2 The confusion and in

tellectual quagmire that has resulted is unfortunate. Proponents of planning innovations through the years-e.g. ,

planned unit development, growth management, transit-supportive development, smart growth, new urbanist,

compact cities, and sustainable cities-are each quick to point out how we might cure sprawl by application of

their ideas. At the same time, critics point out the fuzziness in thinking, the rationa lizations, and the evident fail

ures in past attempts to "correct " sprawl. 3 To clarify this debate , we need a better conceptualization, better defi

nitions and better supporting data.

This paper has three parts. In the first part, I present a conceptualization of the different, indeed conflicting,

ways that we think of urban sprawl. This leads to the idea of a planning efficiency frontier (PEF): a concept that I

use to characte rize an efficient urban area from a perspective commonly ascribed to planners. We can then think

of the shift of an urban area over time either toward or away from the PEF as an outcome of local political centes-


tation. In the second part, I present two measures to assess sprawl. One is a measure of mean local density of

population within an urban area. The second is a measure of the variation in local density within an urban area. I

argue that these two measures are important in characterizing the PEF. In the third part of the paper, I apply

these measures using better supporting data, basically massive amounts of comparable geo-referenced small-area

data from recent censuses, to come up with a novel assessment of sprawl in urban areas in Canada (in 1996 and

2(01) compared to America (in 1990 and 2000). In the final part of the paper, I consider what that assessment tells

us about the outcome of political contestation from one urban area to the next .

I. Conceptualization

In the contemporary social science and planning literature, I find three distinct discourses about urban sprawl.

One is the discourse of residents that sees sprawl as a problem experienced. The second is the discourse of plan

ners that sees sprawl as a problem to be solved. The third is the discourse of social scientists that sees sprawl as

an implication arising from particular ways of theorizing urban growth. I illustrate starting from early writers in the

field .

Whyte (1958) is an early statement on urban sprawl as a problem experienced . Born in then-rural West Chester,

Pennsylvania, near Philadelphia , in 1917, Whyte was a journalist with Fortune magazine who went on to a second

career as a scholar of urban sprawl and revitalization. Whyte characterized sprawl in terms of its adverse environ

mental impacts, and gave it a personal (and, in my view, polemical) twist:

Already huge patches of once green countryside have been turned into vast smog-filled deserts... On theouter edge of the present Philadelphia , some of the loveliest countryside in the world is being irretrievablyfouled...

Whyte (1958, 103)

Arguably, Whyte is ideologically conservative. He had seen his beloved West Chester as the rolling farmland it had

been, and rued the change wrought by urbanization. However, accepting that urbanization was unstoppable , he

then delineated the problem that he saw as urban sprawl:

Because of the leapfrog nature of urban growth, even within the limits of most big cities there is to thisday a surprising amount of empty land. But it is scattered; a vacant lot here, a dump there -no one parcelbig enough to be of much use.

Whyte (1958, 103)

This refocusing brings Whyte to his principal solution:

Reserve open space while there is still some left-land for parks, for landscaped industrial districts, and forjust plain scenery and breathing space.

Whyte (1958, 104)

Whyte proposed the establishment of land banks and land trusts to acquire and manage signif icant pieces of open

space. Since Whyte, numerous authors have written on sprawl as a problem experienced.' Notable here are the

three laments about suburbia in Carver (1962: 12-22); the lament about muddle, the lament about uniformity, and

the lament about what is not there. More recently, Danielson et al (1999, 517) argue simi larly that the Los Angeles

basin is sprawl , despite its density , because it is huge, is an unrelieved fabric of developed land, contains little

open space, and has an over-abundance of low-quality commercial space. While there are evident differences in

perspective here, what these have in common is that Whyte, Carver, and Danielson et al equate sprawl with both

the loss of something (e.g., open space, clean air , aesthetics), tied to the spread of an unrelieved, muddled , or


uniform urban fabric. The implication here is that measures of urban sprawl should look explicitly at the presence

or absence of variation in density and/or the urban fabric acrossspace within an urban area.

Bauer (1956) exemplifies the second discourse: urban sprawl as a problem to be solved. In her case, the perspec

tive is that of a planner.

The wartime boom in babies caught us unaware, but we thought it would be temporary... Here we are, fo cused on old central areas, with a tremendous kit of tools for reconstruction, while the vast flood of newurban development flows beyond our view, all around our chosen island. The wave mounts and mounts.

Bauer (1956: 106)

Why is sprawl a problem? Presumably for dramatic effect, Bauer makes the following (again, in my view , polemi

cal) prediction about urban sprawl: in her words, "rurbanization".

If the next several million people [in the LA basin] are scattered even more widely than the last wave,won't everyone ... spend all day driving from one place to another ...? All our present overwhelming problems of servicing such areas will be multiplied tenfold, and the countryside , that vague ideal for which wehave sacrificed all else, will have moved out into another state. Against this , we would have none of thetraditional urban virtues to console us. For rurbanization is the kiss of death for city and country alike , asanyone who has been in California recently can attest. Although the goal is personal and family freedom ,cum natura, it doesn't quite work out that way.

Bauer (1956: 109)

Bauer, at the time a professor at the University of California at Berkeley, personalized sprawl much as Whyte did

above. However, her practitioner's sensibilities were different. In sprawl , she saw problems of slow and lengthy

trips, the costliness of lot servicing, and the loss of both countryside and urban benefits. The loss of open

space-so dear to Whyte-is not central here. She argues (p 112), polemically in my view, that controlling sprawl

can help "re-establi sh some of the traditional cosmopolitan virtues of urban life which are now lost in the stupid

village ideology and class-race exclusionism practiced in suburbia". Her disdain for features of suburbs that some

residents find attractive is a further indication that she is not looking at urban sprawl simply as a problem experi

enced.

Bauer is just one selection from the extensive planning literature on urban sprawl as a problem to be solved.

Another notable early study is Lower Mainland Regional Planning Board of British Columbia (1956). This Report (p.

8) is specific about how to measure sprawl:"

Sprawl takes many forms, but all forms have one common characteristic-low population density... Sprawl isa stage of transition between true agricultural development, which has a density less than 0.3 people peracre, and suburban residential development , with a density greater than 3.5 people per acre.

The Report argued that sprawl areas, being costly for governments to service relative to the property tax revenue

they generated , were fiscal "deficit areas". The Board recommended a five-year urban growth boundary so that

residential land uses are encouraged inside, and rural land uses outside. 5

In the ensuing years, proponents continued to argue that sprawl is a problem to be solved. Notable here is

Downs (1994) who argues that the typical American consumer wants to own a car and a detached house in the sub

urbs with yard space and clean air , in an environment free from poverty. In Downs' view, the simplest way to think

about sprawl is to equate it with low-density [sub]urban development. Other critics ague that broader measures of

sprawl are needed. Ewing (1997) summarizes the sprawl literature and argues that there are three more charac

teristics of sprawl, in addition to Down's low-density development; these are strip development, scattered devel

opment, and leapfrog development." Note here that the scattered and leapfrog development that Ewing opposes is

. ~ . . --- - - - ....

Urban sprawl and the planning efficiency frontier Page4

conducive to the preservation of open space that Whyte and others find attractive. In fact , to Ewing, reducing the

variation of density in this way is tantamount to reducing urban sprawl.

From urban sprawl as a problem experienced and as a problem to be solved, we see diverse conceptualizations

of the problem and its solution . Although it is not the only way to think about sprawl, population density is at the

heart of many of these conceptualizations. Further, much of the debate about sprawl focuses on the extent of

variation in density across an urban area. Further, there is a fundamental conflict here in the interpretation of a

change in density and its spatial variation. To those who see sprawl as a problem to be solved, an increase in den

sity (a more compact urban area) and a reduction in its variation is often seen to be good. To those who see sprawl

as a problem experienced, an increase in density-whether through intensification, in-filling, or reduction in open

space-and a reduced variation may well be seen as bad.

It is interesting to speculate here as to why planners and residents might have different views. After all, plan

ners are public servants and therefore might be expected to reflect the interests of residents of the urban area. I

don't adhere to a conspiracy theory here; that somehow planners as technocrats want to subjugate the citizenry

and some notion of democratic will. Rather, I think that there is a range of public opinion about what is appropri

ate public policy and that planning tends to draw practitioners who are more supportive of environmental ap

proaches than may be typical of the community as a whole. I am not trying to argue here that this is somehow

wrong where and when it happens. Instead, I argue that different conceptualizations produce political contesta

tion that may well be resolved differently from one political jurisdiction to the next.

Finally, I consider sprawl as an intellectual concept. In a seminal paper that does not even use the term "urban

sprawl", Clark (1951) used a density gradient model to help understand and predict the variation in population

density across the urban area and its changes over time. He used data at the level of Census Tracts for large ,

grOWing urban areas in North America, Europe, and Australia from 1801 to 1947 to draw two generalizations:

In every large city, excluding the central business zone, which has few resident inhabitants, we havedistricts of dense population in the interior, with density falling off progressively as we proceed to theouter suburbs.

2 In most (but not all) cities, as time goes on, density tends to fall in the most populous inner suburbs,and to rise in the outer suburbs, and the whole city tends to 'spread itself out'.

Clark (1951: 490)

The first generalization suggests the presence of sprawl in the sense that newer (outer) suburbs are less densely

populated than older (inner) areas. The second generalization suggests that, with time, low-density suburbs be

come more densely populated. Put differently, in-filling and intensification slowly raise density in the outer sub

urbs. It might seem that Clark is simply describing a processof in-filling that over time gradually causes outer sub

urbs to approach the same density as inner suburbs. However, this is not exactly true. Clark explains his results as

follows.

If a metropolitan area is to have a high total population, it must either put up with a considerable degreeof overcrowding in the inner suburbs, or it must spread itself out ... Spreading out is only possible wheretransport costs are low in relation to the citizen's income.

Clark (1951: 495) .

So, it is the combination of city size and the cost of transportation relative to income that drives the density gra

dient. Note here that the gradient affects the overall density; here larger cities have a steeper gradient and a

higher overall density. The gradient also affects the variation of density across the urban area. Flattening of a

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city's gradient over time leads to a spreading urban area (sprawl) and thus a decrease in variation. The cause here,

according to Clark, is the increasing affluence of households," This causal link then presumably implies also the re

verse; that a reduced level of affluence (as when consumer prices rise faster than consumer incomes) means that

the city's density gradient will then become steeper with the implication that mean density will increase as will

variation within the urban area. A period of great postwar prosperity that began after the Second World War pe

tered out in the late 1970s; since then , we have seen periods and places across Canada and America where real

hourly earnings have declined and others where earnings have risen. Clark's analysis suggests that the density gra

dient should change as incomes change relative to the cost of transportation.

Clark does not speak directly of a time frame , but presumably the perspective here is one of an equilibrium pat

tern of land use achieved over the longer run. Income or the cost of transportation can change in the short run.

However, it takes time for the built form of a city to adjust to such changes. In the short term , landlords may find

it best to retain buildings no longer best suited to market demand and let these deteriorate more rapidly over time

until it becomes profitable to tear them down and build anew. Presumably, in a city whose population is growing

faster , any adjustment will happen faster than in a city whose population is growing less quickly or even declining.

Clark's empirical analysis raises questions of local geographic scale and objectivity. Clark arrayed Census Tracts

by distance from downtown, and then fitted a density gradient model to these data." In so doing, he excluded

large parcels of land used for nonresidential purposes (e.g. , industrial, commercial, or park lands). In this way,

Clark was measuring a kind of "net" density for each census tract; one that measures persons per unit of land used

for housing, local roads, and presumably some residual ancillary land uses. However, it is difficult if not impossible

to identify land use precisely in practice. Clark's approach here appears subjective in that he did not present a sys

tematic or objective method (rationa le) to identify how parcels of land are delineated for the purposes of exclu

sion.

Note also in the three discourses above that there is a dissonance between the concepts of sprawl and popula

tion density. When planners imagine sprawl, they perceive it typically as a problem of built form: too much clut

ter, too much fragmentation of developed land. However, when they measure sprawl, they use population density.

In part, this is because data are available to measure population density whereas there are no similar comparable

data on land use and built form available across the nation. Mindful of this limitation, population density can be a

valuable indicator of sprawl. However, there is a second limitation here in the sense that population density is also

driven by factors other than a change in built form. To give an example, consider the implication of the trend to

ward smaller household size over the last five decades in Canada and America . The implicat ion here is that, in an

urban area in which built form has not changed between two censuses, we would nonetheless still expect to ob

serve that average population density has fallen. Of course, some observers would claim that this instances sprawl.

I don't disagree, but such a claim undercuts the argument that we should measure sprawl using only data on built

form and suggests to me that population density is a useful (although not the only) measure of urban sprawl.

II. Measuring sprawl and its variation

To th is point, I have argued that there are different ways of conceptualizing sprawl. In many (but not all) of

these ways, population density-measured both as overall density and its variation within the urban area-is indica

tive of sprawl. From the point of view of the planner, a density that is low overall and with much deviation implies

sprawl. From the perspective of the resident , the loss of open space and increased homogeneity that typically ac-

Urban sprawl and the planning efficiency front ier Page 6

companies increased population density itself is sprawl; hence, higher and more uniform density (that is, less de

viation) implies sprawl. Either way, if we want to use population density as an indicator of sprawl , we need to be

able to detect as well how much it varies acrossan urban area.

To begin thinking about the definition and measurement of sprawl , consider the following question . Which is

more densely inhabited: Canada or America? Excluding freshwater surfaces, the two nations are similar in land

area. However, in 2001, Canada contained just over 30 million persons, compared to 281 million in America in

2000. Therefore, the ratio of these two-nationwide average (gross) population density-was much lower in Can

ada. However, comparison of such nationwide gross densities is often not helpful in thinking about urban sprawl.

Much of Canada's population resides in a narrow band near the U.S. border. Therefore, local population density, if

measured as the average number of people living nearby, might well be higher in much of Canada compared to

America even though nationwide gross population density is much lower. It is not just nationwide averages that are

problematic here. Even at the level of CMSAs, area-wide gross density measures are misleading. Consider the data

in Table 1 showing gross population density by size of metropolitan area for America in 2000 and Canada in 2001 .

The New York CMSA tops the list of large American urban areas at 783 persons per km2 while the Los Angeles CMSA

is at the bottom (186 persons per km2) .

9 Such density values only weakly evidence the spike in population density

that one might expect to find in the largest urban areas. Interestingly, among Canadian areas of the same size (ex

cept "rural and small urban"), area-wide density is higher than the corresponding American urban areas." None

theless, at both the nationwide and area-wide level , the problem with these gross density measures is that they

include all land within a given jurisdiction even though much of that land might well be unoccupied or unoccu

piable . Such land deflates the average population density as seen by residents who typically must interact within,

and navigate through , the built-up areas. Further, these data provide no informat ion about the variation in density

that I have argued above is essential to many descriptions of urban sprawl.

Suppose instead that we measure population density at a local scale repeatedly across an urban area, and then

from these data obtain a pair of summary stat istics: (i) the mean local population density and (ii) the variation in

local density within that urban area. We could then represent each urban area as a point on a scatter plot. Clark

and his intellectual heirs would argue that the land market would tend toward higher mean densities and a greater

dispersion in density across the urban area as we move from smaller cities to larger cities. Therefore, we would

expect both mean density and its variation to increase with the size (population) of the urban area. From such a

diagram, we could identify "best practice" urban areas as seen by planners: that is, urban areas that, for their size,

combine a high mean local density with a low spatial variation. Best-practice urban areas would form a lower en

velope in this diagram. Following the argument of Clark above, I conjecture that this envelope, a PEF, is an in

creasing function of mean density. I presume here that a low -density area conta ins primarily single detached

housing with little variation in density throughout. In contrast, in larger urban areas, where high central city rents

impel consumers to opt for high densities, we observe a wide range of housing densities across the urban area, and

hence more variation. This PEF is a political battlefield. Over time, planners presumably work to move their urban

area closer to the frontier. At the same time , groups opposed to intensification (including, but not limited to, resi

dents) work to resist such shifts, or even to reduce density still further. As a prelude to understanding the out

comes, it is therefore useful to know which urban areas have moved away from the PEF and which have moved

closer.

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To operationalize this method, suppose that an urban area can be represented on a map as a set of n dots, each

dot i representing a known resident population, PI. A variety of geographic scales are possible here: a dot might

represent a dwelling, a street address, a city block, a block group, a census tract, or even a municipality. In each

case, the dot is a representation (e.g., the centroid) of an area within which people live. For each dot i, suppose

that we now count the number of persons resident at all dots that are within a distance of r km: that is, including

persons at dot i itself plus those any other dots sufficiently nearby. Next, because we count all dots within r km of

a given dot , divide the count of population by the area over which it is calculated : namely nr', This is local den

sity , Vi, at each point i. In turn , LOr is the population-weighted mean value of V, across the n points making up the

urban area.

where

lJ'j = 1 if dij~r, 0 otherwise.

Note here that, since this measure is weighted by the nearby population, parts of the urban area that are lightly

populated have relatively little impact on LOr. In this sense, LOr is the density as experienced by a typica l resident.

In this regard, LOr is therefore relatively insensitive to the drawing of the boundary of urban area to the extent

that the boundary passes through areas that are lightly populated. To measure the variation in LO" I calculate its

standard deviation , S" as follows .

Note here that Sr is also weighted by nearby population .

Since my method assumes that everyone assigned to a dot li ves there (and not simply somewhere nearby), a

large n (f iner spatial disaggregation within the urban area) is better than small n (coarser spatial disaggregation).

In the empirical case study presented here, the finest geographic scale at which comparable Census population

counts are available for all of Canada and America are the Dissemination/Enumeration Area (Canada) and Block

Group (America). These data give population counts and centroid location for dots of typically 200 to 400 house

holds. There were 52,993 dots in the Canadian census in 2001 , averaging 566 persons per dot , and 333,098 dots in

the American census in 2000, averaging 845 persons. In addition to having a larger population on average, Ameri

can Block Groups are also more varied than Canadian Dissemination Areas; see Figure 1. There are relatively more

Block Groups with a small population, as well as relatively more with a large population; in contrast, Dissemination

Areas are more similar in size across the country .

To calculate LOr and S" we need to specify r. While any r is possible, I use r=2 km so as to approximate the no

tion of a "dist rict ". In contrast, a neighborhood is sometimes thought to be an area with a radius of about 5 min

utes walk, or about 400 meters radius. Instead, I use a 2 km radius here because I want to approximate the area

within which a person might expect to drive to do local shopping, go to school, or visit a doctor or dentist. Note

also that, in the absence of complete street network data for Canada, my measure of distance is "as the crow

flies "; I ignore impediments to travel in straight line . In a similar manner, the calculation of LOr employs a circle of

radius r wherein no adjustment is made for surface areas covered by water or otherwise uninhabitab le.


III. Assessment of Urban Sprawl

On average, Canadians live at higher local densities than do Americans." From Dissemination Area data , the av

erage Canadian in 2001 had 22,871 neighbors within 2 km; from Block Group data, the average American in 2000

had only 20,656 neighbors. This gives LD2 = 1,820 persons per km2 for Canada versus 1,644 persons per km2 for

America . See Table 2. Thus, measured locally, density is higher in Canada than in America . At the same time,

there is considerable variation here. The 52 for all Canada in 2001 was 2,016, and for America in 2000 was even

larger at 2,920. These deviations in local density are large because the "dist rict" covered by this measure can

range from a dense urban high-rise neighborhood to a remote settlement in Alaska or Yukon. We might therefore

expect to see less deviation once we restrict our attention to a specific urban area. If indeed urban sprawl is char

acterized mainly by a uniformity of density, we should expect to find much less deviation in affected urban areas.

Before we do that, however, further insights into the comparability of Canadian and American census data are

gained by looking at the cumulative distribution for LD2 in the two nations. See Figure 2. Evident here are two im

portant national-level distinctions between Canada and America . First, in Canada, a higher proportion of the

population lives at low LDz-roughly up to about 80 persons per km2• This corresponds roughly to rural and remote

Canada. In America, the proportion at these low densities is lower. In part, however, this appears to be because of

the way Block Groups are denned.? Second, in Canada, a higher proportion of the population lives at high LD2• LD2

exceeds 1,280 persons per km2 for 50% of Canadians in 2001, compared to only 36% of Americans in 2000. This is all

the more surprising since, as is shown below, no Canadian urban area has the very high mean local density for New

York City,

The breakdown of these national averages by size of urban area in Table 2 is instructive. The means for the size

categories vary substantially in each country. Not surprisingly, mean local density is highest on average in large ur

ban areas, and lower in smaller cities. Further, there is an important difference in mean local density between the

two countries after controlling for size class. In the two intermediate size categories (100,000 - 999,999 persons,

and 1,000,000 - 3,999,999 persons), Canadian urban areas are about twice the density of their American peers. In

fact, I argue below that Canada is exceptional also in the largest size class (4 million persons or more) if New York

City is excluded. Put differently, if we measure sprawl as low-density development, America is experiencing more

urban sprawl than is Canada. The story is similar if we measure, as residents might, sprawl as unrelieved urban

fabric (density invariant from one part of the city to the next). Below, I present a more sophisticated analysis.

However, for the moment , I note simply that 52 in Table 2 is smaller for all sizes of urban area except the largest

in America in 2000 compared to Canada in 2001. Furthermore, sprawl is getting worse in America, at least from a

resident's perspective; 52 decreased for all sizes of American cities between the last two censuses, while it tended

to increase slightly for Canadian cities. In contrast, if we measure sprawl as planners do-infilling within existing

areas-the evidence for 52 would suggest that that planners in America have been more successful at controlling

sprawl than have planners in Canada.

Let us now turn our attention to the largest urban areas individually in the two nations. Table 3 presents com

parative results for the 10 largest American urban areas and the 10 largest (albeit much smaller) in Canada. For

comparison purposes, area-wide population density is calculated as well as the local density measures (LD2 and 52).

Urban areas are listed in Table 3 in order of declining LD2 as of the latest census. This is much different from a list

ordered by area-wide average population density; e.g. , Los Angeles, which would have been near the bottom, is

now near the top of this list. Among the twenty areas, the New York urban area has, not surprisingly, the highest


mean local density. After all, a history of urban development predating automobile-oriented development in the

20th century, a constraining topography (i.e., coastline) and a large metropolitan population help put pressure on

central area rents and land prices, and thereby made necessary a high mean local density . What is perhaps sur

prising is that other large older American urban areas do not also have substantia l mean local densities. Despite

their large sizes, the Philadelphia CMSA ranks only 9th, Boston CMSA is 13th, and the Washington MSA is 15th in the

list in Table 3. Moving westward and southward across America brings us to younger urban areas with less history

of intensive development before the 20th century. For such urban areas, we might well expect lower mean local

densities. Indeed, in the Midwest , Chicago comes 5th in the list, and Detroit is a lowly 18th. In the Southwest,

Dallas and Houston are at the bottom of the list as one might expect, but much-larger Los Angeles ranks fully 4th.

What is also surprising here are the relative positions of the Canadian urban areas. Toronto and Montreal stand 2nd

and 3rd among all the urban areas in Table 3. Vancouver has only one-third of the population of San Francisco, and

yet has a comparable mean local density.

Comparison of the latest and previous census is also telling. 13 In eight of the urban areas, LD2 rose by more than

50 persons/krn/: Dallas, Houston, Los Angeles, New York, and San Francisco in America, and Vancouver, Ottawa

Hull , and Edmonton in Canada. In five of the urban areas, LD2 fell by more than 50 persons/km/: Boston, Detroit,

Philadelphia, and Washington in America and London in Canada. While Table 3 suggests that mean local density

has increased overall over time, clearly some urban areas are exceptions to this.

Consider now the measure of deviation (5 2) presented in Table 3. First, note that the urban area deviations are

generally less than the national values (2,920 for America, 2,016 for Canada in the latest census) in Table 2: only

in New York, Toronto, and Montreal does the urban area variation exceed the respective national variation. Fur

ther, 52 is now typically smaller than LD2 in each urban area.

The fotlowing conclusions can now be drawn from comparisons of these 20 urban areas. First, not surprisingly,

large urban areas have higher mean local densities than do smaller urban areas; local density is also more variable

across the urban area among larger cities. Second, in general, Canadian urban areas have higher mean local densi

ties than American urban areas. Third, deviation in local density within individual urban areas is substantial.

Fourth, while there is evidence that mean local density is rising over time, there are also numerous urban areas

where mean local density hasdeclined.

Consider now the full set of urban areas across America, and their Canadian counterparts. Do the findings for

the top 10 urban areas hold up for urban areas as small as 100,000 persons? Figure 3 plots mean local density

against size for the 247 smaller American and Canadian urban areas: 100,000 to 999,999 persons in size. Figure 4

shows the same information for larger urban areas: 1 million population or more. Figure 3 and Figure 4 show a pro

nounced trend; the larger the urban area, the more densely it is populated . Among the smallest urban areas ex

amined here (under about 125 thousand population), Canadian and American urban areas of the same size typically

have about the same density . It is only at the top end among small urban areas, above 125,000 persons, that Ca

nadian urban areas tend to be relatively more densely populated than their American peers. Also, Figure 4 shows

that larger Canadian urban areas are almost always denser than their American peers.

Across Canada and America, which urban areas are the leaders (high mean local density) for their size and which

are the laggards (low mean local density) from a planner's perspective? To answer this question, I combine and ar

ray by size all American and Canadian urban areas of 100,000 persons or more as of the latest census. There are


290 urban areas altogether here. From this , I then find the subset of these urban areas such that there is no

smaller urban area with a higher mean local density. This subset conta ins the 11 urban areas shown in Table 4.

Since this subset, by definition, always includes the urban area with the lowest population, I ignore the smallest

area (Kokomo). To the remaining 10 areas (i.e., those urban areas that for their size have the highest mean local

density), I then fit a model of the form:

using nonlinear least squares to obtain a=2,741 ,830, b=13,712, c=0.33. Then, I use th is formulate to predict the

"potential density", LD2' , for each of the 290 urban areas in the full sample. The discrepancy between an area's LD2'

and the local density it actually achieves is a measure of the laggard-ness of the area.

Now we are ready to set up the concept of a PEF. Figure 5 presents first the case of the smaller urban areas:

those with a population of 100,000 to 1,000,000 persons. Figure 6 presents similar data for larger urban areas:

1,000,000 population or more. In both figures, we see that 52 is positively correlated with LD2• At lower levels of

LD2 in Figure 5, under about 800 persons per km2, smaller Canadian and American urban areas appear to have a

similar deviation (52)' It is only at higher levels of LD2 that one finds that smaller Canadian urban areas now have

typically a lower 52 than their American equivalents. In Figure 6, larger Canadian urban areas generally also have a

lower 52 than do their American counterparts.

Now, suppose that we consider an urban area of a given size. We can imagine that planners seek to counter

sprawl by increasing LD2 and reducing 52 for that urban area over time. Imagine that there is some maximum LD2

and some minimum 52 that is possible. This would be a point on the PEF. Plausibly, the maximum density might be

approximated by LD2' as calculated above. In a corresponding way, we can th ink of the minimum 52 as being the

lowest 52 that we observe among urban areas that have that level of density. All of the above is predicated on the

idea that the urban area is of a certain size (total population) . If we were to consider urban areas at different

sizes, we would expect the minimum 52 to vary correspondingly. In other words, smaller urban areas would at best

be able to achieve low mean local densities with little variation in land use (because the rent gradient is flatter)

while large urban areas would at best be able to achieve much higher mean local densities and have correspond

ingly greater variation in land use (because the rent gradient is steeper). Therefore, the PEF would be the locus of

combinations of maximum LD2 and minimum 52 for each size of urban area.

There are two ways to find a PEF. One is to invoke a theory of political contestation that could somehow estab

lish for each size of urban area the maximum LD2 and minimum 52 possible. Such a theory is beyond the scope of

this paper. The second possibility is to approximate a plausible PEF. That is the method I employ here. I show, in

Figure 5 and Figure 6, one possibility for the PEF. This shows a minimum level of 52J here denoted 5/, for each

level of LD2• I chose the intercept to correspond to the lowest 52observed among our urban areas, and then chose

the exponent to form a lower envelope of 52 among urban areas in the sample (here including larger urban areas as

well as smaller) . The estimated PEF equation is as follows.

5 • - 200 (LD 0.2454)2 - +exp 2

In Figure 5 and Figure 6, there are 11 urban areas whose 52 lies below the efficiency frontier: even if only by a

small amount. One case is Anniston AL for which 52=196 and 5/=258. I could have chosen a smaller exponent to en-


sure no urban areas lie under the efficiency frontier, but I think of the frontier as an achievable standard that has

already been reached in some urban areas.

Using these two criteria , proximity to LO/ and proximity to 5/, which are the best performing urban areas ac

cording to planners. Panel (a) of Table 5 lists five of the best performers in the latest census from among the 290

urban areas examined ; Panel (b) lists five of the worst. The best performers consist of New York plus four Cana

dian urban areas. In each case, planners might well be proud that these urban areas have a high LOz given their

population size and also have an 5z near 5z". The worst performers include five American urban areas: all in the

Northeast. Presumably, planners generally would not be proud of any of these poor performers; all have a low LOzfor their population size and all have an 5z far away from 5z".

Which cities have moved closer to the PEF: that is, where has LOz increased and 5z decreased from previous to

latest census? In this analysis, I control for boundary changes from one census to the next. I overlay digital bound

ary files for each urban area from the latest census on the block group or enumeration area centroids from the

previous census. This permits me to assign each block group or enumeration area from the previous census to the

urban areas in the latest census, and therefore to recalculate local density and its deviation in America in 1990

using 2000 urban area boundaries; and in Canada in 1996 using 2001 boundaries. I then calculate the change in LOz

and the change in 5z for each "constant boundary" urban area between the previous and latest census. See Figure 7

wherein, once again, each urban area is represented as a point. The horizontal axis there measures the change in

mean local density in each "constant boundary" urban area from previous to latest census (negative if LOz de

clined). The vertical axis measures the corresponding change in 5z•

Those urban areas that move closer to the PEF would be in the lower right quadrant where LOz is increasing

and 5z is decreasing. Note that the lower right quadrant is defined independently of the precise location of the

PEF; wherever the PEF is located , urban areas in the lower right quadrant presumably are moving closer to it. The

lower right quadrant contains the 46 urban areas listed in Table 6. I have broken them down into 4 panels de

pending on how close their LDz is to LO/. Panel (a), which includes only Honolulu, is the set of leaders. Panel (b),

"near leaders", includes other urban areas wherein LOz is as much 500 persons/krrr' below LOz•. The largest urban

areas in panel (b) are Stockton and Modesto. Panel (c), "near laggards" includes urban areas wherein LOz is 500

1000 persons/krn' below LOz". The largest urban areas here are Fresno and Omaha. Finally, Panel (d) , "laggards",

includes urban areas wherein LOz is more than 1000 persons/km/ below LDz". The largest urban areas in panel (d)

are Portland and Nashville. None of the 46 urban areas are Canadian. So, although local density tends to be higher

on average for Canadian urban areas, the evidence suggests that some American urban areas have begun the proc

ess of catching up.

None of the largest urban areas in either Canada or America moved closer to the PEF. To me, this is surprising.

The planning literature contains much praise and enthusiasm for just the kind of infilling and intensification that

would presumably lead to a higher W 2 and a lower 5z• What are the possible explanations for this anomaly? One

possibility, as mentioned above, is that planners are unable to achieve what they want because of political contes

tation. It is difficult for me to assess the validity of this argument because I have no systematic source of informa

tion on political involvement across Canada and America . A second explanation might be that planners are typi

cally responsible for a single jurisdiction (e.g. , a municipal government) within the urban area and therefore are

unable to control sprawl over the larger urban area that we are studying here. This is a question that I plan to ex-


plore further because it is possible to measure local density and its variation within individual municipalities across

the two nations.

At the same time, I note that federal legislation in America in general gives planners authority over areas that

contain multiple municipal jurisdictions. As such, American planners may be better able to control sprawl over a

larger region than are Canadian planners. Perhaps this is why the 46 areas that have moved closer to the PEF are

all American.

Conclusions

Mean local density (lOr) and its deviation (5r) are valuable measures in assessing urban sprawl. Given the ease

with which large quantities of geo-referenced small-area data can now be accessed and manipulated, these meas

ures are simple to implement and make possible interesting comparisons of density among urban areas. Mean local

density is not constrained by the well -known problems with area-wide gross population density measures. It is also

easier to calculate than conventional net population density measures that make it necessary for us to isolate and

remove large parcels of land not in residential use. At the same time, the deviation ($2) in local density gives us a

useful description of heterogeneity of density across the urban area.

I argue in this paper that divergent views about the nature and cause of urban sprawl have led to much politi

cal contestation. On the one hand, planners have generally been supportive of measures that increased density

and these have included in-filling and intensification. I argue that these translate into higher mean local density

and less variation. I have argued here that planners and residents may well see the issue of sprawl quite differ

ently, but that this pair of values (LD2 and $2) is relevant to both groups. For all but the smallest urban areas ex

amined in this study, the Canadian experience with sprawl is different from America. In Canada, mean local den

sity tends to be much higher and less variable than in American cities of the same size; closer to what I have called

above the PEF. Of course, we cannot observe a PEF directly. Nonetheless, this evidence is consistent with the ar

gument that land use planning historically has been more effective in Canada. To the extent that the PEF does in

deed pit the planner's interest in intensification against the resident's interest in preservation and open space, it

would appear that planners have been more successful in Canada than in America. However, I note two counterex

amples in the course of this paper. First are the unusual local densities in New York City : much higher on average

than found anywhere in Canada. Of course, there is no urban area in Canada anywhere near the size of New York

City, and Clark's work suggests that average density will increase with city size. We can only speculate whether,

were a Canadian city the size of New York City , would it in fact have an average density higher than New York City

presently. Second, I have presented evidence above that all of the urban areas that have moved closer , however

haltingly, to the PEF between the last two censuses are American. Yes, it is true that they started from a lower

density than Canadian urban areas and they need to move far to catch up. Why have no Canadian urban areas

moved closer to the PEP. Has the planning effort in Canada now run out of steam, or alternatively run into greater

resistance?

It is beyond the scope of this paper to test and refute alternative explanations. As pointed out in the paper,

part of the reason for this is that density is not j ust a planning outcome. It also reflects changes in living arrange

ment and household size, in income (relative to the cost of t ransportation) , and recent growth in the population of

the urban area. Much work remains to be done. The modest purpose of this paper has been to show that a pair of

measures (LD2 , $2) are useful in helping us think about sprawl.


References

Alonso, W. 1964. Location and Land Use. Cambridge, Mass.: Harvard University Press.

Bauer, C. 1956. First job: control new-city sprawl. Architectural Forum, 105, September 1956, 104-112.

Brueckner, J.K. 1980. A vintage model of urban growth. Journal of Urban Economics, 8, 389-402.

Burchell, R.W., Lostokin , D., Galley, c.c. 2000. Smart growth: more than a ghost of urban policy past, less than abold new horizon. Housing Policy Debate, 11(4), 821-879.

Bussiere, R., and Snickars, F. 1970. Derivation of the negative exponential model by an entropy maximisingmethod. Environment and Planning A, 2, 295-301 .

Calthorpe, P., and Fulton , W. 2001. The Regional City: Planning for the End of Sprawl. Washington, D.C.: IslandPress.

Carver, H. 1962. Cities in the Suburbs. Toronto: University of Toronto Press.

Clark, C. 1951. Urban Population Densities. Journal of the Royal Statistical Society, Series A, 114, 490-496.

Donaldson, D, 1969. The Suburbasn Myth . New York: Columbia University Press.

Downs, A. 1994. New Visions for Metropolitan America. Washington, D.C.: The Brookings Institution.

Danielson, K.A., et al. 1999. Retracting suburbia: smart growth and the future of housing. Housing Policy Debate,10(3), 513-40.

Edmonston, B., and Guterbock, T.M. 1984. Is suburbanization slowmg down? Recent trends in population deconcentration in U.S. metropolitan areas. Social Forces, 62(4), 925.

Edmonston, B., Goldberg, M.A., and Mercer, J. 1985. Urban form in Canada and the United States: an examinationof urban density gradients. Urban Studies, 22, 209-217.

Ewing, R. 1997. Is LosAngeles-style sprawl desirable? American Planning Association Journal, 63(1), 107-126.

Goldberg, M.A., and Mercer , J. 1986. The Myth of the North American City: Continentalism Challenged. Vancouver: University of British Columbia Press.

Gordon, P., and Richardson, H.W. 1997. Where's the sprawl. American Planning Association Journal, 63(2), 275278.

Gordon, P., and Richardson, H.W. 1997b. Are compact cities a desirable planning goal?American Planning Association Journal, 63(1), 95-106.

Guest, A.M. 1973. Urban growth and population densities. Demography, 10(1), 53-69.

Harrison, D., and Kain, J. 1974. Cumulative urban growth and urban density functions. Journal of Urban Economics, 1, 61-98.

Lower Mainland Regional Planning Board of B.C. 1956. Economic Aspects of Urban Sprawl: A Technical Report. NewWestminster , B.C: The Board. 45 p.

Mills, E.S. 1972. Studies in the Structure of the Urban Economy. Baltimore: Johns Hopkins University Press.

Myers, D., ft Kitsuse, K. 1999. The Debate Over Future Density of Development: An Interpretive Review. WorkingPaper WP99DM1. Washington, D.C.: Lincoln Institute of Land Policy.

Rome, A. 2001. The Bulldozer in the Countryside. Cambridge: Cambridge University Press.

Whyte, W.H. 1958. Urban Sprawl. Fortune, January 1958, p. 103.

YC I .. ""IIIYCI .31t..y VI UI ILI311 ~UIUIIIUltl":ll r-I r:-o.:"\.

Urban sprawl and the planning efficiency f ront ier Page 14

Figure 1 Cumulative proportion of dots (Block Groups, Dissemination Areas, or Enumeration Areas) bypopulation resident in dot.

1.00 --.~--- ..•. . .-- - - - - .. ~- .-- - ._ . _._ _ _ _ - _.. - __• -_._._- _ ~.:==-=~==--:::.-:-~~-=. ~._. _. ._..' _ . > . • ~._ '

0.90 +-----------"L-~--___o~'---___o"...=----------------_!

0.80 +---------/-----r--~<----------------------_!

;3 0.70 +--------f--~r-____,r..------------------------~

~

! 0.60 +---- - ---,I---I- ---,r..-- --- - - - - - - - - --- - - - - - - - - - ----'

~"0

r~

r~ f--------7L----f-----------j

v 0.30 +--+~'----+-------------------------------_!

0. 2<l +-h~.-+-------------------------------_i

0.10 .,..- 7'-- ----- - - - ------- - --- - - --- --- - - - - - --j

. us8G (091p OOO:

[_. Canlllda DA 2001 :

1-us8G (090) 1990 ;

i ~ana<1o EA199.6...1

ascc2lOO2000, lOO' 000lOO

0.00 +--- - - - _ - - - - -1

o

Population in Block Group, Oissemination Area, or Emm eration Area

Source U.S. data calculated from 2000 Census of Populat ion and Housing Summary File 1 using summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups. Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census GEOREFdatabase. Calculations by the author.


Figure 2 Cumulative proportion of population by mean local density (L0 2) .

Page 15

1.00

0.90

0.80

0.10

0.10

==4

.-- ..,~::;:~~~ i/: ~~/,........-:"'.......-.'~/~-~ i....-:: '

/ // /

I I,

1/ ,

:

/I ,

fI

I

!

. USBG (091) 20001[_.- canada DA 2001 !i- USBG (090) 1990 i

i ---- canadaEA 1996 I'_ _ ,._._m__~

0.00o 1,000 2,000 3,000 . ,000 5.000 6,000 1.000

LD2 Local density (persons per square kil omet er)

' ,000 ' .000 10,000

Note

Source

LD2 is mean local density measured at 2 km. radius.

U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups. Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census GEOREFdatabase. Calculations by the author.


Figure 3 Mean local density (LD1 ) by size of metropolitan area for comparable smaller American urbanareas in 2000 and smaller Canadian urban areas, 2001.

2,500 .------------------------------~

~~ 1,500 +---..---"---~_ _ --- - --- ------- _____i

b

J11,000+----...-.l,.....::_~:__-=-_:_---~:__----------------_i.J

1,000,000800,000600,000400,000200,000O+------_ --__~-----_-----~-- _i

oPopulation

Note

Source

LD1 is mean local density measured at 2 km. radius.

U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using summary level 091 block groups. Canadian data calculated from the 2001 Census Geosuite database. Calculations by the author .


Figure 4 Mean local density (LOl l by size of metropolitan area for comparable large urban areas: America 1990 and Canada 1996.

i" America 2000Ii. Canada 2001 I

25,000,00020,000,00010,000,000 15,000,000

Populatio n

5,000,000

I

I!..i:

i

!!

• • !

• !

• • •• !• ••.. • • i,t, • .. ••• !

~~ ~..~- ..

Jt· i!

2,000

8,000

7,000

6,000

..! 3,000

1,000

oo

Note

Source

LDl is mean local density measured at 2 km. radius.

U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using summary level 091 block groups. Canadian data calculated from the 2001 Census Geosuite data base. Calculations by the author.

. .~ __.__. " _.. . ._0.


Figure 5 Efficiency frontier (52 versus LD2l for comparable smaller urban areas: America 2000 and Canada 2001 .

2,000~--------------------------

1,800 +--------------------------~

•1,600 +-- - - - - - - - ----- - --- - - - --- - - -'

! .. America 2000

i • Canada 2001 i:-Pla~ing ef ficiency front ie r ;

•••

••. ..•

4OO +------:-JIN.I""J~~.......~----------------i

g 1,400 +--------------------------..,..---~

s~ 1,200 +-- - --- - - - - - - - - - - ---......- ------..- - - ---il:

i 1,000 +------ - --- --- - - - --- - - - - --- --;

j"2 800 +---------"'-_:-<>t_#---'--Y:....:=-----::;~=----------i

~a 600 -t-- - - - -.....-"

200 +---.~----------------------'

2,5002,0001,000 1,500

Local Density (LD2)

500O+-----_----~----_-----~----_i

o

Note

Source

LD2 is mean local density measured at 2 km. radius. 52 is the standard deviation of local density within 2 km. radius. PEF is 52 predicted by planning efficiency frontier at observed ill2•

U.S. data calculated from 2000 Census of Population and HousingSummary File 1 using summary level 091 block groups. Canadian data calculated from the 2001 Census Geosuite data base. Calculations by the author .

. u_" , _ . . . ;:::;J" __ .... _. __ ••__ ._•• __ ... "'" __ .. __........._ ... o . V ' " ""'~ .... vv . """'''''lloOJU.,;) ,,",l;;VOJUIL\;;; UClLO-


Figure 6 Efficiency frontier (52versus L02l for comparable larger urban areas: America 2000 and Canada2001.

8,000 ...-- ----- ------------ --------,

•7,000 +--- - - --- - - - --- - - - --- - - --- - - -'

6,000 +-------- - ---- - - - --- - - - -r'------i

§ 5,000 +--- - - --- - - - - - - - --r---- - - - ------''t<:o~ 4,000 +----- - - - ------ - - - -r--- ------ ,

A~~ 3,000...,;

2,000 +-------0'-- - ---7''--- ----------- - -'

1,000 +-----t-e~'_c_::_--"--="'""--------------------i

i .. America 2000i • Canada 2001

I==:-~la-"_ni ng effic~n<:~_ !~~

8,0007,0006,0003,000 4,000 5,000

Local Density (L02)

2,0001,000o+------~------~------------...;

o

Note

Source

L02 is mean local density measured at 2 km. radius. 52is the standard deviation of local density within 2 km. radius. PEF is 52 predicted by planning efficiency frontier at observed LD2•

U.S. data calculated from 2000 Census of Population and HousingSummary File 1 using summary level 091 block groups. Canadian data calculated from the 2001 Census Geosuite data base. Calculations by the author.


Figure 7 Change in LD2 and 52: America urban areas from 1990 to 2000 , and Canadian urban areas from1996 to 2001 .

·· -500 -

400

Page 20

300

200

sS.c

IE.g~ci -300c...s:.u

·200 300

Change in LD2from preceding cenus

400 500 600;

I-An1erica ~' . Canada ,

Note

Source

LD2 is mean local density measured at 2 km. radius. 52 is the standard deviation of local density within 2 km. radius.

U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using summary level 091 block groups. Canadian data calcu lated from the 2001 Census Geosuite database. Calculations by the author.

.=tILV WI LIIUI L "-il L I ofjI UIU~ .


Table 1 Population , land area , and area-wide population density by size of urban area, America (2000)and Canada (2001).

America, 20004,000,000 persons or more

New York--Northern New Jersey--Long Island, NY--NJ--CT, CMSALos Angeles--Riverside--Orange County, CA, CMSAChicago-·Gary--Kenosha, IL--IN--WI, CMSAWashlngton--Baltlmore , DC--MD·-VA--WV, CMSASan Francisco--Oakland--San Jose, CA, CMSAPhlladelphia--Wllmington-·Atlantic City, PA--NJ--DE--MD, CMSABoston-worcester-Lowrence, MA--NH--ME--CT, CMSADetroit-·Ann Arbor-Flint , MI, CMSADallas--Fort Worth , TX, CMSAHouston-Galvestotv-Brazoria, TX, CMSAAtlanta, GA, MSA

1,000,000 to 3,999 ,999 persons100,000 to 999,999 personsRural or small urban (under 100,000 persons)

Canada, 20014,000 ,000 persons or more

Toronto CMA1,000,000-3,999,999100,000-999,999Rural or small urban (under 100,000 persons)

Population Land area Persons(000s) (km2

) per km2

281,422 9,161 ,927 3192,846 283,181 32821,200 27,065 78316,374 87,944 1869,158 17,941 5107,608 24,803 3077,039 19,083 3696,188 15,372 4035,819 14,574 3995,456 17,004 3215,222 23,579 2214,670 19,956 2344,112 15,861 259

68,672 486,166 14162,758 977,622 6457,145 7,414 ,958 8

30,007 9,012 ,112 34,683 5,903 7934,683 5,903 7936,477 12,244 5298,988 73,485 1229,859 8,920 ,481 1

Source ICPSR series 3194. CensusofPopulation and Housing, 2000 [United States]: Summary File 1,States. Calculations based on aggregation from SUMLEY 091 (block group) by the author.

Statistics Canada. 2001 Geosuite CD-ROM. Calculations by the author.


Table 2 Mean local density and its variation in Canada, 1996 and 2001, and in America, 1990 and 2000,by size of urban agglomeration.

Population ill2 5 2

(00Ds)

America, 2000 281,422 1,644 2,9204,000 ,000 persons or more 92,846 3,304 4,5001,000,000 to 3,999,999 persons 68,672 1,300 988100,000 to 999,999 persons 62,759 801 723Rural or small urban (under 100,000 persons) 57,145 285 328

America, 1990 248,710 1,584 2,8104,000,000 persons or more 61,674 3,846 4,7421,000,000 to 3,999,999 persons 63,102 1,377 1,109100,000 to 999,999 persons 65,837 825 743Rural or small urban (under 100,000 persons) 58,097 270 329

Canada, 2001 30,007 1,820 2,0164,000,000 persons or more 4,683 3,681 2,2741,000,000-3,999,999 6,477 3,102 2,370100,000-999,999 8,988 1,560 1,065Rural or small urban (under 100,000 persons) 9,859 331 432

Canada , 1996 28,847 1,780 1,9604,000,000 persons or more 4,264 3,635 2,2431,000,000-3 ,999,999 6,169 3,046 2,322100,000-999,999 8,505 1,579 1,048Rural or small urban (under 100,000 persons) 9,910 367 456

Note ill2 is mean local density measured at 2 km. radius. 52 is the standard deviation of local den sity within 2 km. radius.

Source U.S. data calculated from 2000 Census of Population and HousingSummary File 1 using summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups. Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census GEOREFdatabase. Calculations by the author.

Page 22


Table 3 Population density in the ten largest urban areas in Canada, 2001, and America, 2000, showingcomparable density in previous census.

Page 23

896 6,787 7,192364 3,635 2,243416 3,634 2,715165 3,012 2,252554 2,904 2,506328 2,602 2,246325 2,638 1,536230 2,266 1,372426 2,498 2,60982 2,157 1,19881 2,030 94889 1,845 1,223

519 2,087 2,146107 1,775 1,299382 1,880 1,60445 1,605 85795 1,686 817

348 1,614 1,098202 1,216 7822151 ,186 700

783 6,855 7,552793 3,681 2,274847 3,632 2,776186 3,200 2,323510 2,892 2,583369 2,872 2,365690 2,826 1,684483 2,246 1,382403 2,231 2,394162 2,123 1,176187 2,032 951200 1,908 1,271399 1,840 2,038216 1,747 1,339307 1,733 1,517100 1,672 918185 1,635 850321 1,404 994234 1,397 940221 1,333 831

Urban area

New York CMSAToronto CMAMontreal CMALos Angeles CMSAChicago CMSASan Francisco CMSAVancouver CMAHamilton CMAPhiladelphia CMSAWinnipeg CMACalgary CMAOttawa - Hull CMABoston CMSAQuebec CMAWashington MSAEdmonton CMALondon CMADetroit CMSAHouston CMSADallas CMSA

Population

(000s)18,0874,2643,327

14,5328,0666,2531,832

6245,899

667822

1,0104,172

6723,924

863399

4,6653,7113,885

Previous CensusLand AD LD2

area(sq km)20,19211,7077,990

87,97214,55319,084

5,6302,718

13,8458,165

10,20311,3478,0436,292

10,27419,0474,19 1

13,40518,40818,046

Population

(000s)21,2004,6833,426

16,3749,1587,0391,987

6626,188

671951

1,0645,819

6837,608

938432

5,4564,6705,222

Latest CensusLand AD LD2

area(sq km)27,065

5,9034,047

87,94417,94119,083

2,8791,372

15,3724,1515,0835,318

14,5743,154

24,8039,4192,333

17,00419,95623,579

Note

Source

AD is area-wide dens ity (persons per square kilometer) . LD2 is mean local density measured at2 km. rad ius. 52 is the standard deviation of local density within 2 km. radius.

U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using summary leve l 091 block groups and 1990 Census STF3a using summary level 090 block groups. Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census GEOREFdatabase. Calculations by the author.

...... ~_, 1 ....... ',..1 I KJ 1 .....1 __ 1.. _ .......... ..... nnn r .._ C"-r-r-o",,_ •• _ .: . 1 • . _ I ,..,.. " " I

Urban sprawl and the planning effic1ency frontier

Table 4 leaders in mean local density for their size: Canada, 2001 , and America, 2000.

Urban area Population LD2

New York CMSA 21 ,199,865 6,855Toronto CMA 4,682,897 3,681Montreal CMA 3,426,350 3,632Vancouver CMA 1,986,965 2,826Honolulu MSA 876,156 2,324Hamilton CMA 662,401 2,246laredo MSA 193,117 1,739ReginaCMA 192,800 1,586Guelph CMA 117,344 1,486Peterborough CMA 102,423 1,001KokomoMSA 101,541 621

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Note

Source

LD2 is mean local density measured at 2 km. radius. Selection of "leaders" is from among 290urban areas in Canada and America that have populations of 100,000 personsor more. Methodis described in text. In this method, the smallest urban area (Kokomo) in the combined sampleis always labeled a leader by th is method.

U.S. data calculated from 2000 Census of Population and Housing SummaryFile 1 using summary level 091 block groups and 1990Census STF3a using summary level 090 block groups. Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census GEOREFdatabase.

•Urban sprawl and the planning efficiency frontier Page 25

Table 5 Good performers and poor performers in Canada, 2001 , and America , 2000, from a planner'sperspective.

LDz 5zPopulation Actual Potential Actual PEF

(a) Good performersNew York 21,199,865 6,855 6675 7,552 6428Toronto 4,682,897 3,681 4033 2,274 2009Calgary 951,395 2,032 2370 951 854Saskatoon 225,927 1,536 1467 736 625Regina 192,800 1,586 1392 625 646

(b) Poor performersRochester 1,098,201 1,006 2486 1,043 434Hartford 1,183,110 971 2549 1,010 423Reading 373,638 1,109 1735 1,322 467Boston 5,819,100 1,840 4336 2,038 760Lancaster 470,658 837 1874 1,090 384

Note

Source

LDz is mean local density measured at 2 km. radius. 5z is the standard deviation of local density within 2 km. radius. PEF is 5z predicted by planning efficiency frontier at observed LDz•

U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups. Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census GEOREFdatabase. Combined set of Canadian and American urban areas includes only those over100,000 population. Calculations by the author.


Table 6 "Constant boundary" urban areas whose L02 rose from previous to latest census and whose 52fell, categorized by leader-laggard status in previous census.

(a) Leader in 1990Honolulu

(b) Near leader in 1990Billings Bloomington College Station FargoGreen Bay Lubbock Merced ModestoSioux Falls St. Joseph Stockton

(c) Near laggard in 1990Appleton WI Asheville Bellingham Clarksville TNDavenport Des Moines Dothan AL Fort MyersFresno Lexington Madison OmahaFort Walton Beach Greenville Jackson Killeen TXPensacola Portland ME Redding CA Santa FeSt. Cloud Wausau

(d) Laggard in 1990Baton Rouge Charleston Daytona Beach Grand RapidsHarrisburg Jacksonville Johnson City KnoxvilleLakeland Little Rock Nashville Portland OR

Page 26

Note

Source

L02 is mean local density measured at 2 km. radius, 52is the standard deviation of local density within 2 krn, radius, Leader: LD2 at or above LD2' , Near leader: LD2 not more than 500 persons/krn, below LD2' , Near laggard: L02 500-1,000 persons/krn, below L02' , Laggard: L02 morethan 1,000 persons/krn/ below LD2'

U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups. Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census GEOREFdatabase. Calculations by the author.


. The financial support of the Social Sciences and Humanities Research Council of Canada (grant 410-00-0769) is grate fUlly acknowledged.

1 Donaldson (1969) considers at length the vi li ficati on of suburbsand sprawl in the popular and scholarly press.

2 See, for example, Ewing (1997) and Burchell et all (2000).

) See, for example, Gordon and Richardson (1997b).

4 In the empirical li terature on sprawl, there is a debate about whether to measure sprawl using the density of population or the density of dwellings. Advocates of the dwellings approach argue that , with the decline in average householdsize in the last century , the samestock of dwellings contains fewer people with the passing of time. Thus, built form ofthe city may remain unchanged, yet population density declines. However, this paper usespopulat ion density measuresthroughout in keeping with much of the literature.

5 Given this approach to the delineation of sprawl, the obvious solution might have been to impose exaction fees thatmake each new property owner bear the full marginal costs of servicing, and thus eliminate the fiscal deficit. Also interesting is that the Report did not suggest that municipalities practise f iscal neutrality by sharply reducing propertytaxes for farms and other land uses that generate a fiscal surplus.

6 Calthorpe and Fulton (2001) similarly argue the importance of the area-wide approach to sprawl. They see inequityand environmental degradat ion as two major policy issues arising from sprawl. They see sprawl as the failure to planthe metropolitan area as networks of communities, of open spaces, of economic systems, and of cultures; theyemphasize, as the antithesis to sprawl , a diversity of communit ies, variety of connect ions, and clearly-defined commonground (open space system, cultural diversity, physical history , and economic character).

7 Since Clark's pioneering work , much has been written on the application of density gradient mdels. These have included great names in quantitative human geography (Berry, Casetti, Dacey, Edmonston, Griffith, Haynes, Mercer, Morrill, Papageorgiou, Yeates) and urban economics (Alonso, Beckmann, Brueckner, Kain, Kau, McDonald, Mills , Muth,Niedercorn, Pines, Richardson, Straszheim). Much of this literature focused on the economic argument as laid out byClark above and elaborated in the Alonso-Muth-Mills approach to urban spatial structure.' Others saw density-gradientmodels arising because of other processes. Bussiere and Snickars (1970) saw density gradients as the outcome of entropy maximization. Guest (1973), Harrison and Kain (1974), and Brueckner (1980) attributed the density gradient tothe historical pattern of urban development.

8 Mills (1972) is famous for a shortcut method in which just two data points are used; the first point being the land areaand populat ion of the central city, and the second point being the land area and population of the entire metropolitanarea. From these two points , It is possible to estimate the parameters of the density gradient model. Mills' sample,which consisted of 18 larger American cities in the period from 1948 to 1963, showed evidence of ongoing urbansprawl. Edmonston and Guterbock (1984) use the same method to look at American cities from 1950 to 1975 and conclude that there was no slackening in the rate of suburbanization (deconcentration) during 1970-75 compared to theearlie r time period.

9 These are calculated as persons per square kilometer of land area, and include both urbanized and non-urbanizedland areas. It is possible to separate urbanized and non-urbanized areas in the 1990 U.S. census , but data for 2000were not available at time of writing. Using persons per square kilometer of urbanized areas would give modestlyhigher densities . Gordon and Richardson (1997) report markedly higher urbanized population densities for 1990, but Ihave been unable to reproduce these from published U.S. census data.

10 The U.S. Census typically uses larger geographic areas to represent urban areas than does the Canadian Census. Forexample, the south shore of Lake Ontario (U.S.) is largely partitioned into just three urban areas (Buffalo-Niagara Falls,Rochester, and Syracuse) whereas the north shore (Canada) includes 8 urban areas (St Catharines-Niagara, Hamilton ,Toronto , Oshawa, Port Hope, Cobourg, Belleville, and Kingston), plus a substantial nonurban area.

11 Edmonston, Goldberg, and Mercer (1985) come to a similar conclusion by looking at density gradient model estimatesfor Canadianand U.S. cities .

12 Practice here appears to differ from state to state. Northern Pennsylvania, for example, has numerous blocks whereLD2 is under 80 persons per km' : there , block groups look like Canadian Enumeration Areas. In contrast , neighboringSouthwestern New York State has no block groups this small.

13 The data in Table 3 are for urban areas as they existed at the time of a census: no attempt is made here to adjustfor changesin the boundary of the urban area from one census to the next.

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