The spatial structure of American cities: The great majority of workplaces are no longer in CBDs, employment sub-centers, or live-work communities

Shlomo Angel; Alejandro M. Blei

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The spatial structure of American cities: The great majority of workplaces are no longer in CBDs, employment sub-centers, or live-work communities

Shlomo Angel *, Alejandro M. Blei

New York University, 196 Mercer Street, Floor PH, New York, NY 10012, USA

ARTICLE INFO

ABSTRACT

Article history:

Received 15 November 2015

Received in revised form 30 November 2015

Accepted 30 November 2015

Available online xxxx

Keywords:

Metropolitan labor markets Transportation and land use policy Urban spatial structure Employment sub-centers Job decentralization Journey-to-work

Urban transport and land use policies are informed by our perceptions of the prevailing spatial structure of cities. This structure can be characterized by five models: The Maximum Disorder model, the Mosaic of Live-Work Communities model, the Monocentric City model, the Polycentric City model, and the Constrained Dispersal model, where the great majority of jobs are dispersed outside employment centers and where workers and workplaces in a metropolitan-wide labor market adjust their locations to be within a tolerable commute range of each other. We examine evidence from a stratified sample of 40 U.S. cities and from the 50 largest U.S. cities in 2000 to show that the latter model best characterizes the spatial structure of contemporary American cities. The Constrained Dispersal model is, in essence, a hybrid model that combines elements of all other models. We found that, on average, only 1 out of 12 people live and work in the same community; only 1 out of 9 jobs is still located in the CBD; and only 1 out of 7 jobs is located in employment sub-centers outside the CBD. All in all, the great majority of jobs—3 out of 4 of them—is dispersed outside employment centers, including the CBD, and is beyond walking or biking distance. Maintaining and increasing the productivity of American cities now require a sustained focus on meeting the travel demands of this great majority of commuters, rather than promoting transportation strategies focused on improving access to CBDs and employment sub-centers, or within live-work communities.

(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Urban transport and land use policies are informed by our perceptions of the prevailing spatial structure of cities. In the abstract, the term urban spatial structure refers to discernible patterns in the distribution of human activity in cities (see, e.g., Anas, Arnott, & Small, 1998). More specifically, it refers to discernible patterns in the distribution of residences and workplaces in metropolitan areas and in the commuting flows that connect them to each other.

When we seek to maintain and improve the performance of our cities—through transport infrastructure investments, through regulatory reforms of zoning and land use, or through taxes and subsidies—it is important to understand the relationships between these interventions and the performance of cities. In this article, we focus on one critical aspect of that performance: their productivity. As we noted in our companion article in this journal, "The Productivity of American Cities", the greatest productive advantage of modern-day American cities is that they form large and integrated metropolitan labor markets. The policy implication of this finding is that the more integrated metropolitan labor markets are, the more productive they are. We should therefore favor policies that increase the overall connectivity of

* Corresponding author. E-mail addresses: sangel@stern.nyu.edu (S. Angel), ablei@stern.nyu.edu (AM. Blei).

metropolitan regions for productive travel, as well as policies that facilitate both residential and workplace mobility, so as to keep workers within a tolerable commute of the most productive jobs they can find.

Such policies would be quite different in cities with different types of spatial structure. In monocentric cities where most people commute to work in the Central Business District (CBD) (see, e.g., Alonso, 1964), we should support commuter railroads, for example—railroads that carry large numbers of commuters to the CBD on radial routes—as well as a dense system of subways, busses and bike lanes within the CBD. In poly-centric cities where most people commute to dense concentrations of workplaces in sub-centers outside the CBD (see, e.g. Garreau, 1991) or to the CBD itself, we should support light rail networks that connect these dense employment centers to each other; a dense system of public transport lines and bike lanes within these employment centers; as well as regulations that permit mixed land uses within them, allowing residences and workplaces to intermingle. And if cities were mosaics of live-work communities (see, e.g. Howard, 1902) we should support regulations that permit mixed land uses, policies that mandate small city blocks that make it easier to walk to work, and policies that promote a network of bicycle lanes throughout the community, giving priority to short-distance local traffic rather than to longer-distance through traffic.

This article questions whether contemporary American cities conform to any one of these three models; and if they do not conform to any of these models but to yet another model of urban spatial structure,

http://dx.doi.org/10.1016/j.cities.2015.11.031

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that too has significant policy implications. In this article we define five candidate theoretical models of the spatial structure of cities and present statistical evidence from the cities we studied that may help readers decide which one of these models better fits the observed spatial realities of contemporary American cities; namely, which model best describes the great majority of residence and workplace locations and the commuting patterns between them; not a small share, but the great majority. This is, no doubt, an important matter for readers to decide because their perceptions of the overall spatial structure of cities informs their ideas about what can and should be done—in terms of public plans and investments and in terms of regulatory reform—to improve their land use patterns and their transportation systems in the coming years; and when we seek to improve them, we should maintain a clear focus on improvements that may benefit the great majority of commuters rather than on idealistic projects, plans, programs and policies that either ignore the great majority of commuters altogether or assume that they will readily change their residences, workplaces and commute patterns in response to grand visions, visions that not grounded in the complex realities of cities as productive workplaces.

The article is divided into four sections. In section I, we introduce five candidate theoretical models that may or may not capture the key attributes of the spatial structure of contemporary American cities. In section II, we present the evidence for favoring one or another of these models. In section III, we examine the implications of our findings for transport and land use policy. Finally, in an Annex, we summarize the sources of data and the methodology used in our study.1

2. Five models of urban spatial structure

Most urbanites spend a substantial portion of their days at home, at their job, and at getting from home to work and back. Where we live and where we work matter a great deal to us; and getting to work and back—although constituting only one quarter of trips we make (data for 2009, AASHTO 2013, Table 2.1, 9) and not necessarily the most enjoyable trips we make—are the most important trips we make. It is those trips that sustain us, and it is those trips that make us, and our cities, productive. In the foregoing discussion, we shall limit ourselves to working people, their homes, their workplaces, and the patterns of travel between them. We will largely focus on the city as the locus of production, and only indirectly on the city as a locus of consumption. And we will limit ourselves to describing the very coarse spatial structure of metropolitan areas in broad brushstrokes, rather than providing a detailed description of their social and economic ecology. In this section we introduce five candidate theoretical models of the overall spatial structure of contemporary American cities.

2.1. The Maximum Disorder model

The first model is the Maximum Disorder model. It stands at one extreme of possible urban spatial structures. It assumes the absence of any forces of attraction or repulsion between residences and workplaces, among residences, among workplaces, or between both and other features of the urban landscape. Where both transport costs and nuisance costs are zero or negligible, we can imagine a city where residences and workplaces are located everywhere, and where randomly located workers commute to randomly located workplaces.

The Maximum Disorder model: Workers' homes and their jobs are

randomly distributed throughout the metropolitan area, and

workers commute from a random residence to a random job.

1 To conserve space, only a summary of the Annex is given in this article. A detailed Annex can be found online at: http://marroninstitutE.nyu.edu/uploads/content/Commuting_and_ the_Spatial_Structure_of_American_Cities,_20_December_2014_Version2.pdf, pp. 41-50.

Fig. 1. The Maximum Disorder model.

This model (see Fig. 1) is the baseline for the study of urban spatial structure, the null hypothesis of statistics. Any claim that observable structure or order does exist in a given city must produce evidence that rejects the hypothesis that this order could have been produced by a random distribution of workplaces and residences connected to each other by random commutes.

2.2. The Mosaic of Live-Work Communities model

The second model is the Mosaic of Live-Work Communities model. It stands at the opposite extreme to the Maximum Disorder model. In this second model, the attraction between residences and workplaces is very strong: commuting costs are very high either because of limited transport technology or because of the strong preferences for working at home or walking or bicycling to work; and everyone working in the community also lives there.

The Mosaic ofLive-Work Communities model: The metropolitan area is a mosaic of discrete live-work communities, where workers' homes and their jobs are all within walking or bicycling distance of each other.

In this model (see Fig. 2), both people and workplaces are also highly mobile: people move as close as possible to their jobs, and workplaces move as close as possible to their employees, eliminating any wasteful commuting. When people lose or quit their job, they either find a new job in the community or move to a new community where their new job is located, so as to remain within walking and bicycling distance to work. When a workplace changes its location, its workforce relocates to the new location as well or is replaced by a new workforce in the new location. These communities can become stable over time—allowing their residents to build trust and accumulate social capital—only if residents can find permanent employment in the community and do not seek more lucrative or more challenging employment in the larger metropolitan labor market. They must also be willing and able to perform all the required jobs in the community without importing workers from other communities. In an important sense, this model was the underlying spatial structure of the ideal city proposed by Ebenezer Howard, the inventor of the self-contained suburb, in his Garden Cities of Tomorrow (1899). And this was the hope of the visionary British planners who built the new towns on the periphery of large cities in the 1940s, 1950s, and 1960s with the expectation that they too would be self-contained live-work communities.

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Fig. 2. The Mosaic of Live-Work Communities model.

2.3. The Monocentric City model

The third model is the Monocentric City model. In this model, all workplaces congregate in a single location in close proximity to each other and possibly in close proximity to a feature of the landscape, a port, a mine, a holy place, or a transport hub. When they do all congregate together, the cost of shipping goods and exchanging services between them is reduced. They can specialize and offer each other a greater variety of products and services. They can enjoy economies of scale in the provision of public works and amenities. They can share risks and form partnerships. And they can benefit from the free exchange of knowledge and ideas and learn from each other. In other words, other things being equal, firms can be more productive when they all congregate at the city center, commonly referred to as the Central Business District (CBD). Workers seeking to live in close proximity to their workplaces, locate their homes around the CBD. New homes, seeking to maximize access to the CBD, locate as close as possible to the CBD, thus gradually forming a circle around it (see Fig. 3).

The Monocentric City model: All jobs are concentrated in the Central

Business District (CBD). All workers—living in concentric rings at

Fig. 3. The Monocentric City model.

greater and greater distances from the CBD—commute on radial routes to their jobs in the CBD.

The classical monocentric model of the city, posited by Alonso (1964), and later by Mills (1967) and Muth (1969), assumes a priori that all jobs must be concentrated at a singular point in the Central Business District (CBD); that all residences are arranged in circular rings around that point; and that workers commute along radial routes to their jobs at the CBD. The monocentric model gives precedence to the strong forces of attraction between workplaces, forces that bring them all together into one central location. Workers are compelled to locate their residences in close proximity to the center, but—because their residences occupy land—as the city grows out they must locate further and further away from their workplaces, incurring higher and higher transport costs. In this model, commuting costs at or near the center are zero or negligible, and average commuting costs increase with city size.

2.4. The Polycentric City model

The fourth model is the Polycentric City model. In this model, workplaces are still pulled together by strong attractions, and they are all concentrated in a number of dense centers dispersed throughout the metropolitan area, not only in the CBD (for a review of the literature on the Polycentric City model, see Lee, 2007, 480-481). In these centers—typically located around transportation hubs with good access to the metropolitan area as a whole—workplaces share local public goods as well as local amenities. They may also benefit from the ability to form partnerships and share a common pool of workers, and from the ability of their workers to share knowledge with each other. Because these centers are distributed in the entire metropolitan areas, they may be closer, on average, to the residences of their workers than the CBD.

The Polycentric City model: Workers commute to a discrete set of

identifiable employment sub-centers—including but not restricted

to the CBD—located throughout the metropolitan area.

The theoretical rationale for all workplaces to concentrate at the city center breaks down on at least three counts. First, competition for land increases its price, compelling firms—especially those that need large amounts of floor space (and ample parking space)—to leave the center for other locations in the metropolitan area. Second, competition for land in the city center creates congestion, compromising its access advantages and encouraging firms to locate outside the city center so as to be more accessible to their workers. Third, the need to rehabilitate, rebuild and refurbish aging city centers as technology, production methods, land values, and cultural habits change is considerably more complex, more time consuming, and more expensive than new construction in 'green fields' in peripheral locations, again pushing new or growing firms to locate in new sub-centers or 'edge cities' (Garreau, 1991) in outlying areas. These centrifugal forces weaken the ties binding all workplaces together at the CBD, pulling workplaces away from the city center and into employment sub-centers located throughout the metropolitan area (see Fig. 4).

The Polycentric City model is to be distinguished from the fifth model of spatial structure, the Constrained Dispersal model, introduced in the next paragraph. Some scholars have opted to blur the distinction between them, grouping them together and focusing only on the distinction between the Monocentric City model and all other models that focus on the dispersion of jobs away from Central Business Districts (CBDs). This is unfortunate, and not only because the two models are quite distinct in conceptual terms but also because the two models have quite different policy implications, as we shall see below.

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Fig. 4. The Polycentric City model.

2.5. The Constrained Dispersal model

The fifth and final model is the Constrained Dispersal model. This model takes into account both the weakening centripetal forces that held the majority of jobs together at the CBD in the Monocentric City model and the emerging inability of employment sub-centers in the Polycentric City model to attract jobs that have left the CBD. The majority of jobs disperse outside the CBD and outside employment sub-centers—"beyond polycentricity," as noted by Gordon and Richardson (1996)—but the weak centripetal forces still acting to attract jobs to each other or to common infrastructure services and amenities constrain the total dispersal of jobs assumed in the Maximum Disorder model. The Constrained Dispersal model postulates a single metropolitan labor market where individual workers locate within a tolerable commute distance to the best job they can find in this market (see Fig. 5). The desire to be within a tolerable commute distance of jobs also constraints the total dispersal of jobs and residences relative to each other assumed in the Maximum Disorder model. Yet workers do not try to minimize the length of their commute assumed in the Mosaic of Live-Work Communities model: closeness to their job is only one of many considerations, and a rather minor one, in their residential location decision. Most workplaces, on their part, locate throughout the metropolitan

Fig. 5. The Constrained Dispersal model.

area so as to be closer to workers and to reduce their land and building costs, and the forces attracting them to each other are altogether weak (see also Gordon & Richardson, 1993 and Lang, 2003), except for their need to share a large metropolitan labor market, and their occasional need to share local public goods such as common infrastructure and amenities.

The Constrained Dispersal model: While the CBD and a small number of employment sub-centers still attract a minority of workplaces, the great majority of workplaces are dispersed throughout a single metropolitan labor market, and both workers and workplaces adjust their locations so that they remain within a tolerable commuting range of each other.

From the perspective of the Constrained Dispersal model, the second critical flaw in the Maximum Disorder model is that it also assumes that distance no longer matters, thus ignoring the most basic raison d'être of cities: bringing people into closer proximity to each other and to a host of job opportunities. It is that need for closeness that had created cities and metropolitan areas in the first place, and it is that need for closeness that gives their commuting patterns their spatial structure. These patterns must necessarily display the preference of workers to be within a tolerable commute time, and hence distance, from their jobs; and the preference of workplaces to be within a tolerable commute time, and hence distance, from their workers. That need for closeness does not imply that jobs and residences must be on top of each other or within walking distance of each other as assumed by the Mosaic of Live-Work Communities model. On the contrary, it only implies that they cannot allow themselves to be too far from each other regardless of the size of the metropolitan area. Thus this model is characterized by longer commute trips than those assumed by the Mosaic of Live-Work Communities model, but by shorter trips than those assumed by the Maximum Disorder model or by the Monocentric City model.

The Constrained Dispersal model is, in essence, a hybrid model that combines elements of all other models. It postulates that the Maximum Disorder model is largely correct, except that in applies only to the great majority of jobs but not to all jobs, and except that commuters and workplaces move to be within a tolerable commute distance of each other. It postulates that the Mosaic of Live-Work Communities model is also correct, except that it only applies to a small minority of people who live and work in the same community. It postulates that the Monocentric City model is also correct, except that only a small minority of jobs rather than all jobs still locate at the CBD. And it postulates that the Polycentric City model is also correct, except that only a small minority of jobs rather than all jobs locate in employment sub-centers, including the CBD. In general, it postulates that the total dispersal postulated by the Maximum Disorder model is constrained by weak, yet effective, attractive forces that bring residences and workplaces closer to each other and by weak, yet effective, attractive forces that brings workplaces closer to other workplaces.

In the next part of this article we present statistical evidence from the cities we studied that may help readers, decide which one of these models better fits the observed spatial realities of contemporary American cities.

2.6. The evidence

The evidence presented here is based on two data sets. The first dataset comprises census-based geographic information on the origins (residences) and destinations (workplaces) of commuters in the urbanized areas of a stratified sample of 40 U.S. cities and metropolitan areas in 2000. The urbanized areas, as we shall see, roughly correspond to the built-up areas of cities. The second dataset comprises geographic information on the share of destinations (workplaces) in sub-centers, including the Central Business District (CBD), in the 50 largest U.S. cities and metropolitan areas in the year 2000, calculated from data obtained

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from Lee (see Lee & Lee, 2014). Details regarding these two data sets and the method used to generate the evidence presented below are given in the Appendix A.

2.7. Visual evidence from a random set of200 origin and destinations pairs in six cities

As the first piece of evidence, we present a set of maps of the urbanized areas of six cities in 2000—Los Angeles, Philadelphia, Atlanta, Boston, Chicago and Houston. Maps of the remaining 34 cities in our sample are visually similar and have been omitted for lack of space. Each of the six maps shows a random sample of200 commutes within the city's urbanized area, represented by straight lines describing the beeline path between an origin and a destination. Destinations are shown as small black dots at one end of the beeline path. Origin and destination pairs that begin and end in the same census tract are shown as small red triangles. The sample is admittedly small, but statistically representative.2 The maps for the six selected cities are shown in Fig. 6.

We can now compare these maps to the five models of the spatial structure of cities presented earlier. The comparisons are only visual comparisons rather than statistical ones, but sometimes a picture illustrates a point better than a statistic. Comparing these maps with the figures shown earlier, we can surmise (1) that these cities are not Mosaics of Live-Work Communities (trips crisscross the entire metropolitan area and most of them are longer than walking or biking trips); (2) that they are not Monocentric (most trips do not have the Central Business District—the CBD—as their common destination); and (3) that they are not Polycentric (most trips have neither any sub-center nor the CBD or as their common destinations). This suggests that American cities may better conform to the Constrained Dispersal model or to the Maximum Disorder model, but the maps shown here are only suggestive in that regard. To better differentiate between these latter two models, we require the more substantial evidence presented in the following section.

2.8. Actual versus expected average commute distances in the sample of cities

In the companion article preceding this one, "The Productivity of American Cities", we introduced the evidence for the existence of a tolerable commute range, a commuting radius, so to speak, within which workers are indifferent to their job location (Getis, 1969). When people change jobs to locations outside their tolerable commute range, they are more likely to move to a new home closer to their job that those who change jobs to locations within it (Brown, 1975). As Clark, Huang and Withers (2003), 201), "[s]imply, if a household is a long distance from the workplace, when the household moves, it is likely to move nearer the workplace". More generally, the longer the commuting distance, the higher the propensity to quit a job or to change residence (Zax & Kain, 1991). This is an important insight and it underscores the Constrained Dispersal model. It requires that workers and workplaces locate at significantly closer distances from each other than the Maximum Disorder model or the Monocentric City model would imply, but at much greater distances than the Mosaic of Live-Work Communities model would imply.

As a second piece of evidence, we examined data on the origins and destinations of commuters by census tract in a stratified sample of 40 American cities. Using these data, we calculated the weighted average beeline commute distance in each city in our sample of 40 American cities. We then compared it with the expected average commute distance

predicted by the models of urban spatial structure presented earlier. Each of the models implies a different average commute distance. Only two of the models—the Polycentric City model and the Constrained Dispersal model—predict average distances that are in the range of the actual average commute distances observed in the sample.

The Maximum Disorder model, for example, postulates that commuters' residences and jobs are located at random throughout the urbanized area and that commuters travel from a random residence to a random job. We simulated that process in each of the 40 cities in the sample and—assuming that commuters travel in a straight line—calculated the average beeline distance between a set of random point pairs throughout the metropolitan area (yellow circles in Fig. 7).3

The Monocentric City model postulates that commuters' residences are located at random throughout the urbanized area and that all commuters travel from a random residence to their workplace in the CBD. We simulated that process in each of the 40 cities in the sample as well, and calculated the average beeline distances between a set of random points throughout the metropolitan area and the city center, assumed to be City Hall (blue circles in Fig. 7). For 39 out of the 40 cities—Miami is the only exception—the average distance to the city center is shorter than the average distance between two random points in the city.

The Mosaic of Live-Work Communities model postulates that commuters' residences and workplaces are located within walking distance from each other and that people, by and large, walk or bicycle to work. To err on the generous side, we postulated that a live-work community could be a circle with a radius as large as 2.0 km. This radius roughly corresponds to the outer radius of an average American city CBD. It can be ascertained4 that the average beeline distance between any two points in such a circle would be 1.8 km. This value for each city in the sample is displayed in Fig. 7 as a light gray circle.

Fig. 8 shows that actual beeline commute distances in our sample of 40 American cities are smaller than those predicted by the Maximum Disorder and the Monocentric City models and larger than those predicted by the Mosaic of Live-Work Communities model. In fact, we can say with 95% confidence that the average actual commute distance for all cities is 10.3 ± 0.9 km. Similarly, we can say that the corresponding average value for the Maximum Disorder model is 24.5 ± 4.6 km and that the average value for the Monocentric City model is 20.1 ± 3.8 km. We also know that the maximum average value for the Mosaic of Live-Work Communities model is 1.8 km. Given these findings, we can reject the hypotheses that the commute distances predicted by all three models are not statistically different from actual commute distances in our sample of cities with a 95% level of confidence. In other words, both the Maximum Disorder model and the Monocentric City model predict average commute distances that are significantly larger than those observed in the cities we studied, while the Mosaic of Live-Work Communities model predicts average commute distances that are significantly smaller than those observed.

This second piece of evidence leads us to reject three of the five models of urban spatial structure—the Maximum Disorder model, the Monocentric City model and the Mosaic of Live-Work Communities model—as faithful descriptions of the spatial structure of contemporary American cities. Given this evidence, however, we cannot reject the remaining two models—the Polycentric City model and the Constrained Dispersal model—as potentially faithful descriptions of the spatial structure of contemporary American cities.

Still, those who refuse to dispense with the Monocentric City model may argue that our test assumed a very strict form of the Monocentric City model, namely that all jobs are concentrated at a point in the city

This graph is drawn with logarithmic scales on both the x-axis and the y-axis.

2 Mean trip distances between the sample of trips and all trips in the 6 cities studied are 4 See Mathematics Stack Exchange online at http://math.stackexchange.com/ not different at the 95% confidence level. questions/135766/average-distance-between-two-points-in-a-circular-disk

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Houston

Fig. 6.200 randomly selected origin-destination commute pairs in six American cities, 2000.

center. This, they may argue, was never the case. If CBDs did not contain all jobs but only the great majority ofjobs and these jobs were scattered over a small area around the city center it may well be that the average distance to jobs at the CBD would not be statistically different than the observed average distance.

2.9. The share of jobs in the Central Business District

The Monocentric City model, in its purely theoretical form, indeed assumes that all jobs are located at a single point in the center of the city. A more relaxed assumption would be that the great majority of

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— Average CBD Share of Jobs for All Cities

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Fig. 7. Theoretical and actual average commute distances in a sample of 40 U.S. cities in 2000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

Fig. 8. The share of jobs in the 50 largest U.S. metropolitan areas that was located in their CBDs in 2000.

jobs—say more than half of all jobs in the city—are located in a small district around the city center, the Central Business District (CBD). Surely, this may have been true before the advent of the private automobile and the truck, but it is certainly no longer the case.5 Yet the belief that most jobs, and hence most commute destinations, are located in the CBD persists among those who still see contemporary metropolitan areas as conforming to the Monocentric City model. Our third piece of evidence, described in this section, seeks to undermine this belief.

Kenworthy and Laube (1999), for example, collected data on commuting patterns in 47 cities, 40 of which had one million people or more in 1990: 13 cities in the United States, 7 in Canada, 6 in Australia, 11 in Europe, and 10 in Asia.6 The share of jobs in the CBD (in a subset of 29 of these cities where data was available) declined significantly7 from 25.4% in 1960 to 21.2 in 1970; it declined significantly again (in a subset of 38 cities where data was available) from 21.5% in 1970 to 18.1% in 1980; and it declined significantly yet again (in a subset of41 cities where data was available) from 18.0% in 1980 to 16.2% in 1990. On the whole, these data strongly suggest that Central Business Districts—loosely defined as the largest concentrations of workplaces—in cities and metropolitan areas the world over may now contain not more than one-fifth of the total jobs in these cities and metropolitan areas.

More recent and more comprehensive evidence on the share of jobs in the CBD in American cities is available from the dataset obtained from Professor Bumsoo Lee for this study (see Lee & Lee, 2014), which includes data on commuting patterns to the CBD and to other employment sub-centers in the 50 largest U.S. metropolitan areas in the year 2000, and described in detail in the Appendix A. The third piece of evidence, showing the shares of all commuter trips with origins and destinations within the urbanized area of the 50 American cities that have the CBD as their destination, is shown in Fig. 8. Eleven smaller cities have a larger share of their total commute destinations in the CBD—greater than, say, 14%—but the relationship between the size of the metropolitan job market and the share of commuter destinations in the CBD is not statistically significant. The average share of jobs that was located in the CBD in the 50 largest metropolitan areas in the U.S. in the year 2000 was only

5 For a review of the literature on the dispersal of jobs away from CBDs, see Anas et al. (1998).

6 The discussion in this paragraph paraphrases Angel (2012), 196-97.

7 The result of a statistical t-test of paired sample for means.

10.8 ± 3.1%. It varied from a maximum of 21% in Austin, and Las Vegas, to a minimum of 4% in Los Angeles. The median value for the 50 cities was 10%, and no city with more than one million jobs had more than 13% of these jobs in the CBD.

Given this overwhelming evidence, we must therefore conclude that the Monocentric City model is not an appropriate model for describing the overall spatial structure of contemporary American cities. Yes, the CBD is indeed the largest concentration of jobs in all American metropolitan areas. But this is a far cry from claiming that the great majority of jobs or, at the very least, half the jobs, is located in the CBD, or that most commuting takes places from the rest of the city to the CBD. We must therefore conclude that the Monocentric City model no longer captures the essence of urban spatial structure in American cities. It is, at best, a description of a small, not to say a marginal, share of commuting behavior in these cities. Needless to say, policies, programs and projects that focus the bulk of political and financial capital on this marginal share will not benefit the great majority of commuters—possibly as many as 90% of them, on average—that do not share the CBD as their destination.

2.10. The share of jobs in sub-centers outside the Central Business District

Even if workplaces are not concentrated in the CBD, there are still good economic advantages for workplaces to be in close proximity to each other and to form clusters or agglomerations. Duranton (2011, 9) summarizes these reasons:

First, a larger market allows for more efficient sharing of indivisible facilities (e.g. local infrastructure), risks, and gains from variety and specialization... Second, a larger market also allows for a better matching between employers and employees, buyers and suppliers, partners in joint-projects, or entrepreneurs and financiers... Finally, a larger market can also facilitate learning about new technologies, market evolutions, or new forms of organization. More frequent direct interactions between economic agents in a cluster can thus favor the creation, diffusion and accumulation of knowledge.

Economists discussing agglomeration economies seldom address the following question: Do businesses seeking to enjoy the agglomeration economies associated with proximity need to locate in a few employment centers—be they CBDs or sub-centers scattered

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throughout metropolitan areas—or do they simply need to locate in the same metropolitan area? If the former is true, then we should expect to see significant clustering of workplaces in employment centers. If the latter is true, then we should expect to see significant de-clustering of businesses and their dispersal throughout metropolitan areas outside employment centers. The fourth piece of evidence presented below should help us decide whether agglomeration economies require the closer proximity offered in employment centers or whether they are features of the metropolitan area as a whole, as already suspected by some scholars (e.g. Gordon & Richardson, 1996).

The Polycentric City model in its pure theoretical form, assumes that all jobs are located in a finite set of employment centers—including the Central Business District (CBD)—scattered throughout the metropolitan area. A more relaxed assumption would be that the great majority of jobs—say more than half of all jobs in the city—are located in well-defined employment centers. If that were true, then the Polycentric City model would capture the essence of the overall spatial structure of contemporary American cities.

Large American metropolitan areas are often conurbations, formed of a number of cities—large and small—that have gradually expanded towards each other to form one contiguous urban expanse. Many of these cities retained their historical downtowns—often well connected to the regional transportation network—as concentrations of workplaces. It should not come as a surprise, therefore, that large metropolitan areas still contain numerous downtowns outside their Central Business District (CBD). The San Francisco Bay Area, for example, contains at least one dozen cities with populations of 100,000 people or more, each with its own downtown forming an employment subcenter. We can refer to those as secondary downtowns.

In addition, the movement of jobs away from Central Business Districts since the mid-1960s, has resulted in the creation of new employment sub-centers, referred to as Edge Cities, a term coined by Garreau (1991). Edge cities are new cities on the metropolitan periphery, not simply expansions of the existing historical cores of cities outside the central city. They are complete 'cities' in the sense of offering jobs, residences, and a full complement of shopping facilities, services, and amenities. And they are top down cities, cities that were created by the actions of a single large-scale developer, to be distinguished from bottom up cities that have emerged from the cumulative actions of a multitude of individual firms and households coming together over time. The developer selects a location with good transportation access to the CBD and to other important destinations; assembles the land; plans the city, usually with the car rather than the pedestrian in mind; obtains the necessary zoning, land use and subdivision and construction permits; invests in infrastructure; oversees the construction of office buildings, homes, shopping facilities, and amenities, all surrounded by ample parking; and sells or leases properties to interested parties, all the while retaining strict control of the development process. Municipal or state authorities may be partners in such ventures and, in some cases, even act as developers: "What is of the essence, however, is that all edge cities were originally the product of decisions by a single large agent; certainly we have uncovered no counter-examples of edge cities created purely through the decisions of atomistic agents" (Henderson & Mitra, 1996, 616). Henderson and Mitra provide a list 9 edge cities—containing only 3 of the 10 largest ones identified by Jarreau—that, as of 1993, created, on average, 14 million square feet of office space each and employed, on average, 65,000 people each. These are large numbers: "As a reference point, cities such as Richmond, Spokane, Memphis, Wichita, Birmingham, Albany, and Little Rock have less than 5 million square feet of office space" (617), the threshold that Jarreau assumed for a concentration of workplaces in a metropolitan area to qualify as an edge city.

A large body of urban economic literature has attempted to define employment centers in U.S. metropolitan areas, to identify them, to count them, and to estimate the number of jobs they contain. A

recent review of the literature (Giuliano, Agarwal, & Redfearn, 2008) lists a large number of studies that have identified employment centers in a great number of American cities during the last two decades. Several authors have noted that the methodology for identifying employment centers is quite arbitrary, and it is certainly true that the ability to detect centers correctly can certainly be improved with further research. Still, most analysts are able to distinguish larger concentrations of jobs with a higher-than-average job density from workplaces that are displaced at low job density throughout large urban expanses.

One of the most rigorous among the many attempts to define employment centers is the one undertaken by Lee (see, e.g., Lee, 2007). We have obtained the original dataset used in Lee and Lee (2014) from Professor Lee and used it to identify and analyze employment centers in the 50 largest American cities in 2000. The methods used by Lee and Lee to identify those employment centers are explained in detail in the Appendix A to this article.

The Lee dataset distinguishes between the Central Business District (CBD) and other employment sub-centers, but does not distinguish between secondary downtowns and edge cities. For the purpose of this section, we group the latter two categories together, referring to them as employment sub-centers or, more generally as sub-centers, to distinguish them from the CBD. We seek answers to two questions. First, what is the share of all jobs in the city in employment sub-centers? Second, what is the share of all jobs in the city in employment centers including the CBD?

The average share of jobs that was located in employment subcenters outside the CBD for the 50 largest metropolitan areas in the U.S. in the year 2000 was 13.8 ± 2.0% (see Fig. 9). It varied from a maximum of 34% in Los Angeles, California, to a minimum of 2% in Providence, Rhode Island. The median value for the 50 cities was 12.8%, and 8 cities other than Los Angeles had more than 20% of their jobs in employment sub-centers: Columbus, Detroit, Dallas, Houston, San Antonio, Tucson, San José, and San Diego. 13 cities had less than 10% of jobs in employment sub-centers. The relationship between the size of the metropolitan job market and the share of commuter destinations in employment sub-centers was found to be statistically insignificant.

We can now pose the central question of this section: What is the share of all commuter trips with origins and destinations within the urbanized areas of American cities that have employment centers including the CBD, as their destination? We can answer this question by examining Fig. 10. In this figure, we simply added the values shown earlier in Fig. 8 to the values in Fig. 9. The average share of

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Fig. 10. The share of jobs in employment sub-centers including the CBD in the 50 largest U.S. metropolitan areas in 2000.

jobs that was located in employment centers including the CBD for the 50 largest metropolitan areas in the U.S. in the year 2000 was 24.6 ± 1.8%. It varied from a maximum of 38.5% in Los Angeles to a minimum of 13.9% in Providence. The median value for the 50 cities was 23.5%, and 9 cities other than Los Angeles had more than 30% of their jobs in employment centers including the CBD: Columbus, Detroit, Dallas, Houston, San Antonio, Tucson, San José and San Diego. The New York metropolitan area, the largest metropolitan area in the United States, had only 23% of its jobs in employment subcenters including its CBD. Fifteen cities had less than 20% of their jobs in employment centers including the CBD. The relationship between the size of the metropolitan job market and the share of commuter destinations in employment sub-centers was again found to be statistically insignificant.

On average, therefore, only one-quarter of jobs in contemporary American metropolitan areas are located in employment sub-centers including the Central Business District (CBD), and in no city does this share exceed 40%. In other words, the great majority of jobs—three quarters of them, on average, are located outside employment centers, dispersed throughout metropolitan areas. This suggests that the Poly-centric City model—while certainly an improvement over the Monocentric City model—is still an implausible description of the overall spatial structure of contemporary American Cities. The Constrained Dispersal model—the model that assumes that only a small share of jobs remain in employment centers, bound by weak attractive forces—appears to be a more appropriate model for describing urban spatial structure.

The evidence presented here also confirms the thesis advanced by Gordon and Richardson (1996): Agglomeration economies in American cities are largely properties of entire metropolitan areas than of smaller clusters within these metropolitan areas. One may ask, however, what about Silicon Valley, that heavy concentration of computer programming and software establishments in a small part of the San Francisco Bay Area? Is not that an example of clustering at the sub-metropolitan level? The map in Fig. 11 shows the location of computer programming and software establishments in the San Francisco Bay Area in 2013.8 This map shows that programming and software establishments are not clustered at all. Surely, there is a small, dense cluster in the San Francisco Central Business District (CBD) and a denser distribution of firms in the San José metropolitan

area and along the western edge of the San Francisco Peninsula, north and south of Palo Alto. There is also a denser concentration of establishments in Berkeley and Oakland in the East Bay. All in all, however, we must conclude that while computer programming and software establishments in the United States may indeed be clustered in the San Francisco Bay Area, they are not found in dense employment sub-centers there but are dispersed over very large areas throughout the metropolitan region.

In general, given this evidence we may conclude that employment sub-centers have failed to attract the large majority of jobs that had migrated out of Central Business Districts over the years, allowing workplaces to disperse everywhere, forming large and integrated metropolitan labor markets. The Polycentric City model thus fails to provide a viable description of American metropolitan areas at the present time. Clearly then, policies, programs and projects that take that model for granted and focus the bulk of political and financial capital on employment centers, say on connecting employment centers to each other by fixed-rail rapid transit, will not benefit the great majority of commuters—as many as 75% of them, on average—that do not share these employment centers, including the CBD, as their destinations.

2.11. The share of commuters who live and work in the same community

The fifth and last piece of evidence presented in this article pertains to the validity of the Mosaic of Live-Work Communities model as a useful description of the spatial structure of contemporary American cities. This model, in its pure and ideal form, views metropolitan areas as a set of small, discrete and self-contained economies, so to speak, with all commuting trips taking place within them and no commuting trips taking place between them. In contrast to all other models of urban spatial structure discussed in this article, this model assumes that the different types of agglomeration economies in large cities that give them a productive advantage over smaller ones—and, more particularly, "a larger market [that] also allows for a better matching between employers and employees, buyers and suppliers, partners in joint-projects, or entrepreneurs and financiers" (Duranton, 2011, 9)—can all be internalized in small live-work communities.

We define the Live-Work Index as the ratio of commuting trips that both begin and end in the community and all commuting trips that either begin or end in the community.9 Again, we assume that an abstract live-work community is a circle with a 2-kilometer radius, roughly the size of an average CBD in an American city.10 The average beeline distance between two locations in such a circle is 1.8 km, a distance that may lengthen to 2.25 km along streets. Such a distance may be traversed in 30 min by walking at 4.5 kilometers per hour, in 15 min in public transport at an average speed of 9 kilometers per hour, and in as little as 10 min by bicycling at 13.5 kilometers per hour.

Fig. 12 shows that the average value of the Live-Work Index (LWI) for all cities in the sample was 7.7 ± 0.8%, and that all these cities had average LWI values that were below 15%. More specifically, it shows that in 35 out of 40 cities in our stratified sample—and in all cities with urbanized areas in excess of 550 km2—the average value of the Live-Work Index was less than 10%. We can conclude, therefore, that on average, for American cities as a whole, less than 10% of commuters live and work in the same community; more than 90% live in one community and work in another. In fact, in only one city in the sample,

8 Custom computer programming service establishments in the North America Industry Classification System (NAICS) code 541511.

9 A detailed description of the methodology used to calculate the average values of the Live-Work Index for the 40 cities in our sample is given in our working paper, online at: http://marroninstitute.nyu.edu/uploads/contEnt/Commuting_and_the_Spatial_Structure_ of_American_Cities,_20_December_2014_Version2.pdf, pp. 28-32.

10 It is important to note that the Live-Work Index varies significantly with the size of communities: the larger their area, the larger the value of the index. This puts into question the results obtained by Cervero (1996,492-511), for example, who calculated a variant of the Index for 23 cities in the San Francisco Bay Area, cities that varied dramatically in area—from San José (457 km2) to Daly City (20 km2).

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Fig. 11. The location of all software establishments in the San Francisco Bay Area, 2013 (Geographic Research, Inc., 2014).

Columbia SC, did we find a single live-work community where more than half of commuters, 58% to be precise, both lived and worked. Four cities in the sample—Boston, Nashua, Portland ME, and Ashville NC—had single communities where more than one-third but less than one-half of commuters both lived and worked; and in all other 35 cities in the sample, there was not even a single community to be found where more than one-third of commuters both live and worked there. Given this evidence, we must reject the Mosaic of Live-Work Communities model as a viable description of the spatial structure of contemporary American cities.

2.12. Summary and conclusion

The evidence presented in this second part of the article allows us to draw a number of important conclusions.

The Maximum Disorder model is not a viable description of the spatial structure of contemporary American cities because (1) the average beeline commute distance in the 40 cities in the sample predicted by the model is 24.5 ± 4.6 km, a significantly longer distance than the

observed average commute distance in these cities, 10.3 ± 0.9 km; and (2) the model predicts that jobs will be dispersed throughout metropolitan areas and that there will be no concentrations of jobs, but there are significant concentrations of jobs, both in the Central Business Districts (CBDs) of cities (10.8 ± 3.1% of all jobs, on average) and in employment sub-centers (13.8 ± 2.0% of all jobs, on average).

The Mosaic of Live-Work Communities model is also not a viable description of the spatial structure of contemporary American cities because (1) the average beeline commute distance predicted by the model, 1.8 km, is significantly shorter distance than the observed average commute distance in these metropolitan areas, 10.3 ± 0.9 km; and (2) on average, in our stratified sample of 40 American cities in 2000, only 7.7 ± 0.8% of commuters lived and worked in the same community. Namely, more than 90% lived in one community and worked in another.

The Monocentric City model is also not a viable description of the spatial structure of contemporary American cities because (1) the average beeline commute distance predicted by the model for the 40 cities in our sample is 20.1 ± 3.8 km, a significantly longer distance than the

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observed average commute distance in these metropolitan areas, 10.3 ± 0.9 km; and (2) the model assumes that the great majority of jobs are located in Central Business Districts (CBDs), while, in the 50 largest American cities in 2000, only 10.8 ± 3.1% of all jobs, on average, were found in CBDs. The great majority of jobs—8 out of 9 jobs, on average—were located outside CBDs.

The Polycentric City model is not also a viable description of the spatial structure of contemporary American cities because (1) the model assumes that the great majority of jobs are located either in employment sub-centers scattered throughout the metropolitan area or in CBDs. On average, only 13.8 ± 2.0% of jobs in the 50 largest American cities in 2000 were located in employment sub-centers, and only 24.6 ± 1.8% of all jobs were found either in employment sub-centers or in CBDs. The great majority of jobs—3 out of 4 jobs, on average—were dispersed outside employment sub-centers or CBDs.

We can conclude, therefore, that only the Constrained Dispersal model is a viable description of the spatial structure of contemporary American cities because (1) the model predicts that both commuters and workplaces will relocate so as to be within tolerable commuting range of each other. It thus predicts that average commute distance in cities, found to be 10.3 ± 0.9 km in a stratified sample of 40 American cities in 2000, will be significantly shorter than those predicted by the Maximum Disorder model or by the Monocentric City model, found to be 24.5 ± 4.6 km and 20.1 ± 3.8 km respectively, and significantly longer than the predicted average commute distance—1.8 km—in the Mosaic of Live-Work Communities model; (2) the model predicts that the dispersal of jobs throughout metropolitan areas will be substantial—involving the great majority of jobs—significantly more than that the dispersal predicted by the Monocentric City and the Polycentric City models (0%) yet significantly less than that predicted by the Maximum dispersal model (100%). In the 50 largest U.S. metropolitan areas in 2000 we found that 75.4 ± 1.8% of jobs—3 out of 4 of jobs, on average—were dispersed. The great majority of jobs were dispersed, as predicted by the model, yet their dispersal was constrained by agglomeration economies of one kind or another keeping one-quarter of all jobs, on average, clustered together in employment centers.

The Constrained Dispersal model is, in essence, a hybrid model that combines elements of all other models. It postulates that the Maximum Disorder model is largely correct, except that in applies only to 3 out of 4 jobs and not to all jobs, and except that commuters and workplaces move to be within a tolerable commute distance of each other. It postulates that the Mosaic of Live-Work Communities model is also correct

except that it only applies to 1 out of 12 jobs, rather than to the great majority of jobs. It postulates that the Monocentric City model is correct, except that it applies only 1 out of 8 of jobs rather than to the great majority of jobs. And it postulates that the Polycentric City model is also correct, except that it only applies to 1 out of 4 jobs rather than to the great majority of jobs. In general, it postulates that the Maximum Disorder model is constrained by weak, yet effective, attractive forces that bring residences and workplaces closer to each other and by weak, yet effective, attractive forces that brings workplaces closer to other workplaces.

3. The implications for transport and land use policy

The future of our cities is path dependent: The cities of the future will evolve from the cities we have already built and, barring catastrophes and calamities ofone kind or another, any changes in their spatial structure and their built form are likely to be gradual and marginal, building upon their existing spatial structure as characterized by the Constrained Dispersal model. The same observation also applies to commuting patterns: Most commuting patterns are quite likely to be between dispersed residences and dispersed workplaces for a long time to come.

The conclusion of our companion article, "The Productivity of American Cities", was that American metropolitan areas now function as single, integrated labor markets where workers and workplaces are matched at a truly metropolitan scale. We concluded that the most important productivity advantage of larger cities is the larger size of their labor markets and the greater choice it offers both workers and workplaces. The policy implications of these findings are that the more integrated metropolitan labor markets are, the more productive they are. We should therefore support policies that increase overall regional connectivity; policies that allow for speedier rather than slower commuting, for more rather than less commuting, and for longer rather shorter commuting to take advantage of metropolitan-wide economic opportunities.

Given the results of this article, we can now look more closely at the relationship between the productivity of American cities and their spatial structure. We can begin to ask ourselves: Are cities that have a larger share of their jobs and residences clustered in CBDs, in employment sub-centers, or in live-work communities more productive or less productive than cities that conform to the Constrained Dispersal model?

Our provisional answer to this question, in the absence of rigorous evidence to the contrary, is that the advantages offered by clustering are now largely metropolitan in scale. Namely, the agglomeration economies associated with clustering—a large and diverse labor pool, knowledge exchange within industries and across different sectors, shared infrastructure, shared inputs, shared services and amenities, a diverse industry mix that reduces economic shocks, and the presence of large, internal markets are all metropolitan in scope rather than pertaining to concentrations of people and jobs within metropolitan areas. This conclusion is shared by a number of other authors (see, e.g., Burger, Van Oort, Frenken, & van der Knaap, 2009; Gordon & McCann, 2000; Johansson & Quigley, 2004; Phelps & Ozawa, 2003). We concur, except for allowing for those rather weak effects that create and maintain CBDs and those rather weak effects that create and maintain employment sub-centers. We refer to them as 'weak' largely because they could not hold back the decentralization and dispersion of the great majority jobs into the suburbs and then away from employment centers altogether. They could only constrain them, preventing them from eventually creating an even more dispersed spatial structure that would have better conformed to the Maximum Disorder model.

We could only find evidence, albeit rather sparse, that supports our contention and no evidence to counter it. Lee and Gordon (2007a), Lee and Gordon (2007b), for example, did not find that the share of jobs in the CBD or in employment sub-centers affected metropolitan population or employment growth, both of which can be considered indirect proxy variables for the productivity of cities. Meijers and Burger,

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in one of the only empirical studies that explored the effects of urban spatial structure on the labor productivity of U.S. cities, concluded that "[metropolitan areas with more dispersion do not perform worse in terms of labor productivity" (2010,1398).11 Our own rather elementary multiple-regression test of the 50 largest U.S. metropolitan areas in 2000 in Lee's dataset, with labor productivity measured in metropolitan area GDP per worker as the dependent variable and (1) the number of jobs in the city, (2) the average density of jobs in the city, (3) the share of jobs in the CBD, and (4) the share of jobs in employment subcenters as independent variables found that only the number of jobs in the city had a significant effect on labor productivity. The shares of jobs in the CBD or in employment sub-centers did not.

As for the productivity of live-work communities, we may recall the insight of Alonso who responded to President Johnson's endorsement of "a balanced and beautiful community—not only a place to live, but a place to work as well. It will be largely self-contained, with light industry, shops, schools, hospitals, homes, apartments, and open spaces" (February 1968, quoted in Alonso, 1970, 38) by noting that

seeking closure at a small scale may economise on certain inputs (such as those of commuting) but results in lower per capita production (and lower disposable income after accounting for commuting costs) as well as the risks of instability and low adaptability which affect small cities. In small cities a declining firm can be a local disaster, new firms are less likely to develop because of the sparseness of linkages, a dismissed worker has fewer chances for re-employment, a boy has fewer career opportunities, a woman fewer choices for shopping, and so on. In short, trying to save on transport costs may be penny-wise and pound-foolish (Alonso, 1970,44)

A recent article in the Economist reached a similar conclusion: "the lesson of the new towns is that being linked into a bigger city fosters growth.... The notion that they would be self-contained economies has largely failed" ("Paradise Lost", The Economist, 3 August, 2013). This newer lesson confirms that Greater London, as expected, benefits from metropolitan-wide agglomeration economies that cannot be captured in self-contained live-work communities. In short, self-contained live-work communities can be expected to be less productive than large metropolitan regions with integrated labor markets.

In the absence of rigorous evidence to the contrary, we cannot conclude that the Constrained Dispersal model of urban spatial structure in inherently less efficient and less productive than the Monocentric City model, the Polycentric City model, or the Mosaic of Live-Work Communities model. This does not necessarily commend it as optimal in any way. In truth, the Constrained Dispersal structure of American cities has been enabled by—we might even say has come into existence by—the car (and the truck), abetted by tax and subsidy policies favoring highways and single-family homes and by regulatory regimes favoring low-density 'green field' development. And this has come at a price, the price exacted from cities conforming to this spatial structure becoming dependent on the car and the truck for their continued productivity and prosperity. This symbiosis between the highly dispersed spatial structure of American cities and the highly efficient door-to-door long-distance commute offered by the private automobile is reflected by the current statistics of the travel times and modal choices of commuters: According to the 2013 American Community Survey (U.S. Census, 2014) the national average travel time to work was 25.1 min and only 7.5% of all commuters required more than one hour to reach their workplace. Out of a total of some 138 million workers, 86.1% used a private automobile (of which 10.0% shared one), 5.0% used public transit (of which 2.2% used fixed-rail transit and 2.8% used busses), 0.6% bicycled to work, 2.9% walked to work, and 4.3% of worked at home (1.2% used other modes: taxi, ferry, motorcycle etc.).

11 We should note that Meijers and Burger's study referred to the dispersion of populations and not to the dispersion of jobs.

It is not difficult to conclude that the continued reliance on the private automobile for travel to work and the increasing dispersal of workplaces away from the CBD and away from employment sub-centers represented by the Constrained Dispersal model are mutually reinforcing. The ready availability of cars makes it possible for workplaces to disperse throughout the urban area—occupying low-rise buildings on cheaper and lower-taxed land with ample parking in less congested neighborhoods—without sacrificing their productive edge; and the formation of large metropolitan labor markets, accompanied by the dispersal of jobs away from the CBD and away from employment subcenters, requires the great majority of workers to travel to work by car—usually beyond walking and biking range but within a tolerable commute range of their chosen place of residence—to reach the better paying and more productive jobs available to them in the metropolitan area as a whole.

Acknowledging the symbiosis underlying the productivity of contemporary American metropolitan areas is in no sense an endorsement of the continued use of the private automobile as we know it today, neither for urban travel in general nor for commuting and business travel in particular. Much can be done to improve its performance, to reduce its carbon emissions, to automate it, to price its use correctly, and even to make it driverless; and much can be done to improve the use of the road network through better use of road space, through better traffic management, through correct road pricing and through the completion of the road network with additional links. The key prerogative for us is to understand that the productivity of American cities as they have come to be relies on efficient long-distance door-to-door transport among dispersed locations, a function that at the present time can be fulfilled only by the private automobile and by no other mode. Transportation improvements and investments should therefore focus, as an important policy priority, on improving or replacing the private automobile with a better, more efficient and more environmentally friendly alternative; a more equitable one that is not careless about the carless. In American cities with a Constrained Dispersal spatial structure, neither fixed-rail rapid transit (with or without feeder busses), nor busses, nor bicycles offer attractive alternatives to meet the commuting needs of their integrated metropolitan labor markets, where three quarters of jobs are scattered in dispersed locations throughout the metropolitan area.

That said, we must reduce our reliance on the private automobile as we know it today. We have arrived at a juncture in the lives of our cities and metropolitan areas where their continued productivity may hinge on reigning in greenhouse gas emissions in general—and those produced by cars in particular—so as to slow down global warming. In all probability, reigning in greenhouse gas emissions would entail reducing overall mobility. Mobility has been broadly defined as "the ability to travel where you want when you want, to connect to places in the metro area you might want to go" (Staley & Moore, 2009,4). Commuting accounts for only one-quarter of total travel and, of necessity, constitutes a dimension of metropolitan mobility that warrants a special policy focus. Indeed, making commuting more efficient or more equitable is quite different from a focus on enhancing or reining in mobility at large.

Transportation policies can facilitate commuting by promoting transport modes and routes that help the great majority of actual commuters get to work—from their actual homes to their actual workplaces—rather than by focusing on transport modes and routes that help relatively few, perhaps at the expense of many. We must weigh the benefits of favoring local travel or linear travel to employment centers against the cost of restricting metropolitan-wide travel, or more generally, the prospect of harming the majority of commuters by promoting plans that serve a minority. We must insist that any deliberate policy change in land use and transportation patterns must ensure, at the very minimum, that it does not improve a small part of the urban land use and transportation system while risking its overall productivity. Small agendas, enticing as they may be, must give way to

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the broader ones, those that aim to preserve and sustain the productivity and vitality of our great metropolitan areas.

At their best, land use and transportation policies contribute to the productivity of metropolitan areas when regulations, taxes and subsidies, and public investments respond to two complementary forms of demand: First, they respond to the demand for unrestricted residential and workplace mobility, namely the demand of workers and workplaces to move freely from one location to another so they can be within tolerable commuting ranges of each other. Second, they respond to the demand for the best fit between workers and workplaces, namely the demand of workers to reach their most productive choice of workplace during the morning rush hour and to return to their homes during the evening rush hour quickly and economically. The dominance of the Constrained Dispersal model in contemporary American metropolitan areas informs us that, for the great majority of commuters today, responding to this second form of demand calls for regulations, taxes and subsidies, and public investments that support longer-range metropolitan travel between dispersed locations, namely travel beyond walking and biking distance between dispersed residential and job locations outside the Central Business District (CBD) and outside employment sub-centers.

There appears to be no escape from the conclusion that some form of long range door-to-door conveyance—an improved yet unrealized version of the private automobile of today—is the transportation mode best suited to the spatial structure of both present and future American cities, a spatial structure best characterized by the Constrained Dispersal model and one that cannot be expected to change in radical ways any time soon. It is long-range door-to-door conveyance that both gives form to these cities and sustains and maintains their very large metropolitan labor markets, integrated labor markets that now form the very core of their unparalleled agglomeration economies, economies that are the very foundations of their productivity. We conjecture that the future prosperity of American cities in the coming decades may rest on an improved

version of this long-range door-to-door conveyance, rather than on replacing it with other, less effective transport modes: increasing its energy efficiency, decreasing its reliability on non-renewable fossil fuels, making better use of road space, and increasing traffic safety—possibly through the conversion of the car fleet to driverless vehicles, vehicles that can also serve those who cannot drive and do not require parking in congested areas.

A final note of caution: Most of the data used for this study is for the year 2000. In the intervening 15 years, a number of important changes have occurred, raising the question as to whether our conclusions still hold. One of the more important changes has been the recent revival of city centers and CBDs as centers of employment:

The analysis of recent U.S. Census data suggests that downtown employment centers of the nation's largest metropolitan areas are recording faster job growth than areas located further from the city center.... Over the four years from 2007 to 2011, we found that city centers—which we define as the area within 3 miles of the center of each region's Central Business District—grew jobs at a 0.5 percent annual rate. Over the same period, employment in the surrounding peripheral portion of metropolitan areas declined 0.1 percent per year. When it comes to job growth, city centers are out-performing the surrounding areas in 21 of the 41 metropolitan areas we examined. This "center-led" growth represents the reversal of a historic trend of job de-centralization that has persisted for the past half century (Cortright, 2015).

Surely, this development is to be applauded. But lest readers put too much hope in the radical reversal of the patterns of urban spatial structure reported in this study, they may recall similar hopes generated by Garreau's Edge City now-famous announcement in the early 1990s: "The bulletin is this: Edge Cities mean that density is back". Lang (2003), reporting on Edgeless Cities a decade later, confesses that "he is not especially happy to deliver the latest bulletin: the long-standing

Fig. 13. Locations of the 40 cities in the sample.

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Table 1

Characteristics of the 40 U.S. cities in the sample.

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Urbanized area Label

New York-Newark NYC

Los Angeles-Long LAX

Beach-Santa Ana

Chicago CHI

Philadelphia PHI

Miami MIA

Dallas-Fort DAL

Worth-Arlington

Boston BOS

Washington DC DOC

Detroit DET

Houston HOU

Atlanta ATL

San Francisco-Oakland SFO

Cleveland CLE

Pittsburgh PIT

Portland POR

Virginia Beach VRB

Sacramento SAC

Kansas City KSC

Columbus CLM

Austin AUS

Hartford HRT

El Paso ELP

Omaha OMA

Albuquerque ALB

Grand Rapids GRP

Columbia CLB

Des Moines DES

Spokane SPO

Pensacola PEN

Jackson JAK

Shreveport SHR

Ashville ASH

Tallahassee TAL

Nashua NAS

Portland PME

Norwich-New London NOR

Kennewick-Richland KEN

High Point HPT

Pueblo PBL

Tyler TYL

State(s) Population, 2000

NY, NJ, CT 17,799,861

CA 11,789,487

IL, IN 8,307,904

PA, NJ, DE, MD 5,149,079

FL 4,919,036

TX 4,145,659

MA, NH, RI 4,032,484

DC, VA, MD, DE 3,933,920

MI 3,903,377

TX 3,822,509

GA 3,499,840

CA 3,228,605

OH 1,786,647

PA 1,753,136

OR, WA 1,583,138

VA 1,394,439

CA 1,393,498

KS, MO 1,361,744

OH 1,133,193

TX 901,920

CT 851,535

TX, NM 674,801

NE 626,623

NM 598,191

MI 539,080

SC 420,537

IA 370,505

WA 334,858

FL 323,783

MS 292,637

LA, AL 275,213

NC 221,570

FL 204,260

NH, MA 197,155

ME 180,080

CT 173,160

WA 153,851

NC 132,844

PA 123,351

TX 101,494

Area, 2000 Population group (km2)

8683 1

4320 1

5498 1

4661 1

2891 1

3644 1

4497 1

2996 1

3267 2

3355 2

5083 2

1364 2

1676 2

2208 2

1228 2

1364 2

1514 3

1030 3

1216 3

presence of 'edgeless cities' means that sprawl is back—or, more accurately, that it never went away" (2003,1). Unfortunately, we have not been able to examine more recent data on the spatial structure of American cities, nor have we been able to uncover more recent findings that question our conclusions. The primary data does exist, however, and it is possible to repeat our analysis along the same lines with 2015 data, a task we plan to undertake in due time. We do confess, however, that we do not hold high hopes for radical changes in the spatial structure of American cities as we have come to understand it.

American cities have now evolved a highly dispersed spatial structure and a highly flexible door-to-door long-distance commute system that are in a symbiotic relationship with each other: the door-to-door long-distance commute system both serves and generates this spatial structure and that spatial structure, in its turn, requires the door-to-door commute system to support and enhance it. Interventions aimed at improving the land use and transportation system in American cities in the coming years must acknowledge this symbiotic relationship as well as its durability before acting to change it for the better in both marginal and radical ways.

Acknowledgments

The authors wish to thank Professor Bumsoo Lee of the University of Illinois for graciously sharing his dataset on employment sub-centers.

Annex. A stratified sample of 40 U.S. urbanized areas and the identification of employment centers

A random stratified sampling procedure was used to select 40 Urbanized Areas from the universe of all 242 U.S. cities that had populations of 100,000 or more in the year 2000. This universe of cities was ranked by population size in descending order and partitioned into five groups, so that each group contained roughly twice the number of cities in the previous group. Eight cities were then randomly selected from each group to obtain the final sample. A map displaying their locations of the 40 selected cities is shown in Fig. 13. Their names, three letter labels, populations and areas, and are given in Table 1. The identification of employment sub-centers in the 50 largest Urbanized Areas in the year 2000 was based on a dataset created by Lee (see Lee & Lee, 2014). This information allowed us to calculate the number and share of jobs in the CBD, in sub-centers outside of the CBD, and outside sub-centers.12

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The spatial structure of American cities: The great majority of workplaces are no longer in CBDs, employment sub-centers, or live-work communities Academic research paper on "Social and economic geography"

Abstract of research paper on Social and economic geography, author of scientific article — Shlomo Angel, Alejandro M. Blei

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