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The productivity of American cities: How densification, relocation, and greater mobility sustain the productive advantage of larger U.S. metropolitan labor markets

Shlomo Angel *, Alejandro M. Blei

The Urbanization Project, Stern School of Business, New York University, 196 Mercer Street, Floor PH, New York, NY 10012, USA

ARTICLE INFO ABSTRACT

The greatest productive advantage of modern-day American cities is that they form large and integrated metropolitan labor markets. We present new evidence on the importance of self-adjusting commuting and location patterns in sustaining the productive advantages of larger metropolitan labor markets, mitigating the difficulties in coping with their sheer size, and reducing the added burdens on their transportation infrastructure. As a result of these adjustments, the metropolitan labor market—defined as the actual number of jobs in the metropolitan area reached in less than a 1-hour commute—is almost twice in size in a U.S. city with a workforce twice the size. More particularly, in a U.S. metropolitan area with twice the population of another one, commute time should be expected to increase by a factor equal to the square root of 2. Instead, it only increases by one-sixth of that factor because of three types of adjustments that take place as cities grow in population: increases in residential density, locational adjustments of residences and workplaces to be within a tolerable commute range of each other, and increases in commuting speeds brought about by shifts to faster roads and transit systems. 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 of two kinds: first, those that increase overall regional connectivity and 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; and second, policies that remove impediments to the locational mobility of residences and workplaces for all income groups so that they can easily relocate to be within tolerable commute range of each other.

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license

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

CrossMark

Article history:

Received 11 November 2015

Received in revised form 26 November 2015

Accepted 30 November 2015

Available online 21 December 2015

Keywords:

Metropolitan transportation policy Labor markets Journey to work Agglomeration economies Scaling

1. Introduction

It is generally understood that the main force propelling cities into being and then fueling their growth is their productivity. But in the heated debates on the future of our cities in general—and of our transportation systems and land use patterns in particular—the specific and indeed essential role of our urban transport networks and our urban spatial structure in maintaining and enhancing the productivity of our cities is often misunderstood or rendered ambiguous (see, e.g. Litman, 2014). That said, there appears to be growing interest in integrating economic development goals in transportation and land use planning in American metropolitan areas. A recent white paper issued by the U.S. Department of Transportation, for example, acknowledges that economic development—"a fundamental societal goal of promoting growth in prosperity, economic opportunity, and the population's standard of living"—is "emerging as a priority topic in metropolitan area planning" (U.S. DOT, 2014, 1). It is our firm belief that a renewed focus on the

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

productivity of cities as a key objective in transportation and land use planning is indeed welcome. That said, the relationship between productivity on the one hand and transport and land use systems on the other is often misunderstood. The aim of this article is to bring a new understanding of this critical nexus to the fore.

How productive are American cities? The total amount of goods and services produced in the two largest metropolitan areas in America, New York and Los Angeles, in 2012—their combined Gross Domestic Product (GDP)—was 2.9% of that of the world at large. In comparative terms—to get a sense of the importance of the productive dimension of these cities—their combined GDP was also larger than that of India in that year, $2.1 versus $1.9 trillion (in current US$, World Bank, 2014; BEA, 2013, Table 1). Surely, these two metropolitan giants had many productive advantages over other places.

One of their most important advantages was that they functioned as integrated economies, and they were more productive as integrated economies because they were large. Why? In large part because larger metropolitan areas have larger metropolitan labor markets: workers have access to a larger, more diversified and more specialized pool of jobs, and firms have access to a larger, more diversified and more

http://dx.doi.org/10.1016/j.cities.2015.11.030

0264-2751/© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Table 1

Reasons for intra-county move by type of move, 2008-2009.

Source: U.S. Census, 2011. Geographical Mobility 2008 to 2009, P20-565, November,

Table 7,16.

Reason to move Percent

Family-related reasons 26.5

Change in marital status 5.5

To establish own household 11.6

Other Family reason 9.5

Employment related reasons 8.9

New job or job transfer 2.1

To look for work or lost job 1.0

To be closer to work/easier commute 5.0

Retired 0.2

Other job-related reasons 0.7

Housing-related reasons 57.2

Wanted to own home, not rent 6.6

Wanted new or better home/apartment 18.6

Wanted better neighborhood/less crime 6.2

Wanted cheaper housing 13.9

Other housing-related reason 11.9

Other reasons 7.5

To attend or leave college 1.5

Change of climate 0.1

Health reason 1.4

Natural disaster 0.5

Other reason 4.1

specialized pool of workers. These advantages—coupled with other agglomeration economies or, more specifically 'urbanization economies', such as shared knowledge, shared services and suppliers, shared infrastructure and facilities, shared risk of rapid changes in firm size, or increased competition—give larger cities their productive edge. As our study will demonstrate, metropolitan labor markets in the United States are held together by nimble and self-adjusting commuting patterns between self-adjusting residence and workplace locations that ensure that larger cities do not lose their productive advantage because of the added costs of long commuting trips along congested transport networks. And while commuting constituted only 28% of person vehicle miles traveled (VMT) by all modes (data for 2009, AASHTO, 2013, Table 2.1, 9), highly efficient commuting and location patterns that keep workers and workplaces within an acceptable commute range lie at the heart of the high productivity of American cities in general, and its larger metropolitan agglomerations in particular.

It stands to reason, therefore, that concerns for the effective contribution of commuting and location patterns to sustaining the continued productivity of American cities must guide future urban transport and land use policy, informing decisions regarding government spending, regulation, taxation, investment, and research. The central aim of this article is to present evidence that will shed new light on the key role that self-adjusting commuting and location patterns play in supporting metropolitan labor markets and hence in sustaining the productivity of cities. This evidence will hopefully inform a more pragmatic and more realistic conversation on the possible futures of urban transportation and land use, a conversation that may determine whether we can make the commuting and location patterns ofthe future—so critical to maintaining and enhancing the productivity of our cities—more efficient and more sustainable at the same time. At the end of the day, the productivity of our cities must be harnessed to secure their environmental sustainability, and our cities must become more sustainable so as to maintain their productivity.

The article is divided into three sections. The first section focuses on the relationship between metropolitan labor markets and city size. We introduce data from the U.S. Bureau of Economic Analysis for 347 U.S. metropolitan areas to show that the larger the city, the more productive its workforce. We argue that actual versus potential access to jobs is the key to understanding the size of metropolitan labor markets. We find that the metropolitan labor market—defined as the actual number of jobs in the metropolitan area reached in less than a 1-hour commute—increased by 97%, i.e. almost doubled, in a U.S. city with

twice the workforce of a smaller one, while the share of jobs that were reached within that time declined by a meager 1%.

The second section of the article introduces and discusses the relationship between commuting time and city population size. In theory, other things being equal, average commute time should increase by the square root of 2 (i.e. by 41%) for a city twice the size in population, as we shall explain below. The key finding in this section is that actual commute time in a U.S. metropolitan area with twice the population of a smaller one is about one-sixth of the expected increase of 41%. We believe that observed actual increases are much lower because of three types of adjustments that take place in larger cities: increases in average residential density, the locational adjustments of residences and workplaces to be within a tolerable commute range of each other, and increases in commuting speeds brought about by shifts to faster roads or modes. Larger U.S. cities are indeed denser than smaller ones, bringing workers closer to their jobs than they would be if densities were the same. Workers and their workplaces in larger U.S. cities move closer to each other to mitigate the increased average distance between any two locations in their larger areas, so that the time and distance of commutes remain within workers' tolerable commute range, their preference to remain within a limited time and distance from their workplaces when they select a residence or a workplace. And commuters in larger cities travel at higher average speeds on faster roads—freeways, for example, as against arterial roads—so that average commuting time increases at a slower rate than average commuting distance when city populations increase. The compound result of these three mutually reinforcing adjustments is that in a city with twice the population of a smaller one, commuting time is not 41% higher, as expected, but only 7% higher.

The third section ofthe article presents our conclusions and their implications for future urban transportation and land use policy in American cities.

In Annex A, we map and list the 40 cities in our stratified sample.1

2. Metropolitan labor markets and city size

2.1. The larger the city, the more productive its workforce

Urban theorists in general, and the economists among them in particular, have long sought to explain the emergence and growth of cities. Economists, as early as Smith (1776) and Marshall (1890), recognized that cities bestow productivity advantages on both firms and workers. Marshall suggested three possible sources of these advantages: sharing of inputs, labor market pooling, and knowledge spillovers. More recent research (for a survey of the literature, see Duranton & Puga, 2004; Rosenthal & Strange, 2004) examines a wider range of possible sources and there is now a broad literature focusing on different sources. Duranton and Puga classify these sources into sharing, matching, and learning mechanisms. Sharing includes sharing infrastructure and facilities, input suppliers, larger local markets, and risks as well as gains from variety. Matching mechanisms focus on the matching of firms to workers that allows for specialization, the focus of the present article. Learning is facilitated by bringing together large number of people, enhancing both knowledge generation and its diffusion. Other scholars focus on increased competition and the resulting survival of more productive firms as additional mechanisms for improving productivity (e.g. Combes, Duranton, Gobillon, Puga, & Roux, 2012), or on industrial culture and local institutions as important contributors to productivity differences (e.g. Saxenian, 1994). Most of the literature suffers from the inherent difficulty in isolating the partial contributions of these

1 A more detailed Annex introducing the data sets and discussing the methodology underlying this study can be found online at: http://marroninstitute.nyu.edu/uploads/ content/Commuting_and_the_Productivity_of_American_Cities,_20_December_2014.pdf, pp.32-39.

Fig. 1. Average real GDP as a function of the average population of Metropolitan Statistical Areas (MSAs) in 349 U.S. MSAs, 2001-2014.

Fig. 2. Average real GDP per capita as a function of the average population of Metropolitan Statistical Areas (MSAs) in 349 U.S. MSAs, 2001-2014.

different factors, as well as from the difficulty in measuring the spatial extent of their influence.

As noted above, one of the more important explanations for the higher productivity of large metropolitan areas—and one not sufficiently appreciated by transportation and land use planners and by other urban policy makers—is that larger metropolitan areas have larger labor markets and this bestows upon them a great economic advantage, and possibly the most important one, over smaller ones. Urban economic theory since Smith and Marshall predicts that the larger the labor market, the greater the productivity of both firms and workers. Firms in larger cities have a larger—and, in addition, a more diverse—pool of workers to choose from and can therefore employ workers that are better fitted to the firm's specific requirements. The more fit workers are for their prospective jobs, the less on-the-job training they require, and the more valuable they are to the firm. Taken together, the firm's employees can then be more specialized, allowing the firm to reap the benefits of the division of labor and to become more productive. The firm thus becomes more profitable and can pay its workers better wages and salaries.

In addition, large and diversified labor markets also allow firms to withstand both positive and negative shocks by quickly changing their labor profiles through hiring and firing workers. They allow firms to quickly fill vacancies. They also allow younger firms to experiment with different labor profiles before settling on the most productive ones. Workers, on their part, can choose from a greater pool of jobs, allowing them to find the jobs most suitable for their skills, aptitudes and temperaments, and income expectations. They also allow workers to find jobs that allow them to interact with knowledgeable workers, speeding up their learning, expanding their contact networks, and therefore their job prospects and their future earnings. The higher productivity of firms and the higher wages of workers attract more firms and more workers, thus enabling larger cities to continue to grow their economies and their populations.

Several measures of the productivity of cities have been proposed. Some scholars have preferred wages while others have preferred rents. Some have opted, as we have here, for gross domestic product per capita, while others—pointing to the possibility that this measure would be tainted by larger cities used capital more efficiently (Moomaw, 1983) or employed inherently more productive workers—have opted for more refined measures, measures that require better and more disaggregated data.

Since the early 1970s, many scholars have tried to measure the elasticity of urban productivity with respect to city population, seeking answers to the following question: By what factor is the productivity of

a city with twice the population of a smaller one greater than the productivity of a smaller one? Shefer (1973) estimates this factor to be 1.14-1.17; Sveikauskas (1975) estimates it to be 1.06-1.07; Foggarty and Garofalo (1978) estimate it to be 1.10; Moomaw (1981) estimates it to be 1.027%; Nakamura (1985) estimates it to be 1.034; Tabuchi (1986) estimates it to be 1.043; and Lobo, Bettencourt, Strumsky, and West (2011) estimate it to be 1.011.

Clearly, one of the simplest methods to measure the productivity of U.S. cities is by the Gross Domestic Product (GDP) of their Metropolitan Statistical Areas (MSAs), published annually by the U.S. Bureau of Economic Analysis (See, e.g. BEA, 2015). The average real GDP for the years 2001 -2014 for each MSA as a function of the average population during those years is plotted in Fig. 1 for all 348 MSAs for which complete data is available. The average real GDP per capita for the years 2001-2014 for each MSA as a function of its average population during these years is plotted in Fig. 2.2 Fig. 1 shows that the Real Gross Domestic Product of a city with twice the population of a smaller one increased by a factor of 2.16. The relationship between the total economic output in a metropolitan area and its population is exceedingly strong, with nearly 96% of the variation in GDP explained by population alone (R2 = 0.96). Fig. 2 shows that real GDP per capita—our summary measure for the productivity of cities—increased by a factor of 1.08 in a metropolitan area with twice the population of a smaller one. That relationship is weaker, but still statistically significant (R2 = 0.21) and the factor is in the range observed by other scholars.3 Given these robust results, we must conclude that the larger the city, the more productive its workforce.

2 These two graphs, like all graphs that appear in subsequent pages, are drawn with logarithmic scales on both the x-axis and the y-axis. The data is fitted with a power function of the general form y = ax1, where a and b are constants. The linear regression equation that best fits the data is obtained by taking the logarithms of both sides of this equation, Ln(y) = bLn(x) + Ln(a), or Ln(y) = bLn(x) + c which is a linear equation, and that is why theregres-sion line in the log-log graph is a straight line. The power function shown in Fig. 1 for the Real Gross Domestic Product (GDP), G, as a function of the population of the metropolitan area, P, is G = 0.0209P1113 (R = 0.96), so that G(2P) = 0.0209(2P)1113 = 21113G(P) = 2.16G(P), namely the real GDP of a city with double the population P is 2.16 times the real GDP of the city with population P. The corresponding function for real GDP per capita, Gc, shown in Fig. 2, is Gc = 20.94P0113 (R = 0.21), so that Gc(2P) = 1.08Gc(P).

3 It is important to note that this factor varies from year to year. While the average for the years 2001-2014 was indeed 1.08, the factor was 1.086 in 2001; it then declined gradually to 1.075 by 2009, increasing to 1.081 by 2014. Similarly, the strength of the relationship between real GDP per capita and population, measured by the adjusted R2 of their linear regression equation, decreased from a high of 0.22 in 2001 to a low of 0.15 in 2009, increasing again to 0.18 by 2014, while remaining highly significant in all periods.

2.2. Actual versus potential access to jobs: a clarification

Although metropolitan areas are more productive the larger they are, they cannot and do not grow without limit. Larger cities occupy larger areas. Workers in larger cities may therefore face longer commuting distances to their workplaces and—if travel speeds do not increase sufficiently to compensate for these longer distances—longer commuting times as well. The added distance—and hence the added time and cost—of commuting in larger metropolitan areas are not insignificant and may compromise the economic advantage larger cities enjoy over smaller ones because of their larger workforce and the larger number of jobs they offer. Prud'homme and Lee (1999,1853), for example, suggest that.

[I]n large cities, the effective size of the labor market is very different from the total number of jobs in the city. In Seoul, the average worker has in 60 minutes access to only 51 percent of the jobs offered by the city; and the average enterprise has only 56 percent of the workers in less than 60 minutes.

If that were indeed true, it would mean that the actual size of Seoul's metropolitan labor market is only half the size of its workforce, thus compromising the great productive advantage that its large workforce could provide. Our study of a stratified sample of 40 U.S. metropolitan areas in 2000 suggests that, at least in the case of the U.S, this may not be the case. We find that the size of metropolitan labor markets in U.S. cities—defined as the actual number of jobs in a metropolitan area reached in less than a 1-hour commute—almost doubles in a city with twice the number of workers than a smaller one. In other words, in a U.S. city with a workforce of some 2.5 million, e.g. Philadelphia, 91% of workers reached their jobs in less than 60 min. In a U.S. city with twice that workforce, e.g. Los Angeles—a city that had a similar size workforce to that of Seoul studied by Prud'homme and Lee—90% of workers reached their job in less than 60 min, 60 min being an arbitrary tolerance range for a commute. These percentages are considerably higher than those observed by Prud'homme and Lee in both Korean and French cities. Why?

One possible reason could be that U.S. cities in general, and Los Angeles in particular, have better and faster transportation systems than that of Seoul, as well as higher residential and workplace mobility. That may well be the case, but it would only explain a part of the difference in the data. The key difference in the data is in how one measures the size of a metropolitan labor market. Prud'homme and Lee, as well as other urban economists studying metropolitan labor markets (e.g. Melo, Graham, Levinson, & Aarabi, 2012) use a different metric for measuring the overall size of these markets than the one we use: the average number of potential jobs available from a given residence within a given time limit, say a one-hour commute; and to calculate the average accessibility to jobs in a city with this metric, they effectively assume that particular workers cannot move to a different residence to get closer to their particular jobs. In their perception of metropolitan labor markets, the location of a given residence must be fixed, and access to jobs is then calculated as the average access to job locations from all the fixed locations of residences in the city.

But any potential measure of the size of metropolitan labor markets ignores two important facts. First, most potential jobs—even within one's own industry, so to speak—are not of interest to particular workers who commute to their particular jobs. Second, as we shall see in Section 3 below, particular workers can and do adjust the location of their residences to get within a tolerable commute range of the jobs of their choice. In other words, the location of their residence is not fixed. Indeed, metropolitan labor markets are shaped and reshaped by the locational choices of firms and residences and by the travel choices that commuting among them requires. These choices create a dynamic equilibrium that can and typically does keep jobs within reach of workers and workers within reach of jobs, regardless of the size of

metropolitan areas. Hence, while the number of potential jobs within, say, a one-hour commute of all fixed locations cannot and does not increase indefinitely with the size of city's workforce, the number of actual jobs reached within that time limit does indeed. We thus define the size of metropolitan labor markets not by the potential access to jobs they may offer but by the actual number of workers in the metropolitan area that reach their jobs within a given time constraint, say one hour. Thus, the reason that we estimate U.S. metropolitan labor markets to be much larger than those measured by others is that our definition measures actual access to jobs of real-world commuters rather than access to potential jobs by would-be commuters from fixed residential locations. It may indeed be true that in Seoul, a worker may only have half the jobs in the city at a tolerable commute range from her fixed location, but with one residential move she may have access to most of the other half.

We should keep in mind that if workers can relocate then the whole country, and possibly the whole world, can be taken to be a single labor market. This is true, and in certain industries, say genetic engineering or professional soccer, this is already the case. For most jobs, however, this is not the case. Long-distance relocation is typically costly and not without risk, especially when the new job is insecure. It may require a change of climate and language, separation from family members and friends, a new job for one's spouse and a new school for ones' children, as well as high search costs in strange faraway places and a long period of adjustment to an unfamiliar environment. Such costs and risks are greatly reduced when one moves within a metropolitan area that is already familiar, where information on jobs, houses, and schools is easier to come by. Craigslist, to take one example, organizes its want ads and job offers in lists that closely approximate a metropolitan labor market.

The question remains whether metropolitan labor markets are singular—namely consisting of a single labor market for the entire metropolitan area—or segmented in space into several relatively independent sub-markets. Commuting data on origins and destinations in our sample of 40 U.S. cities can shed some light on this question. In Fig. 3, 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 of 200 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.4

The maps for these six representative cities begin to suggest that, in each and every city, the residences and workplaces of commuters do not congregate to form spatially distinct labor sub-markets. Commuters travel from residences throughout the metropolitan area to workplaces throughout the metropolitan area, implying that the metropolitan area is a single labor market. That said, more advanced spatial statistics are needed to confirm these results and to identify outliers that do not conform to the overall pattern. The Philadelphia metropolitan area may be one of them: The Delaware River—dividing it in two from the southwest to the northeast—appears to break the metropolitan labor market into two distinct sub-markets. That said, our preliminary investigations confirm that this example may be the exception rather than the rule. In general, American metropolitan areas, large and small, are single, integrated labor markets. And it is this unity that gives them their productive advantage.

4 Mean trip distances between the sample of200 trips and all trips in the 6 cities studied are not different at the 95% confidence level.

Fig. 3.200 randomly selected origin-destination commute pairs in six American cities, 2000.

2.3. Metropolitan labor markets and city population size

Given our definition of metropolitan labor markets, we found a very strong relationship between the share of jobs that are actually reached within a given commute time and the total number of commuters in a U.S. city. Fig. 4, calculated from the U.S. Census Transportation Planning Package Part I dataset for 2000, shows the share of workers that could reach their jobs from their homes within a given commute time in five cities, one from each of the five population groups in our sample

of40 cities: Chicago (3.9 million commuters), Philadelphia (2.4 million), Kansas City (700,000), Pensacola (155,000) and Pueblo (52,000). The figure shows, for example, that in all four cities, more than 90% of jobs could be reached in less than 60 min; that 80% of the jobs in Chicago and 85% in Philadelphia could be reached in less than 45 min; and that 60% of the jobs in Chicago, 70% in Philadelphia, and more than 80% in Kansas City, Pensacola and Pueblo could be reached in less than 30 min. Similar cumulative distributions of commute times for all 40 U.S. cities in our sample were used to create the graphs in Figs. 5 and 6.

Fig. 4 The share of workers with commutes that are shorter than a given commute time in five representative cities from the sample of 40 U.S. cities, 2000.

Fig. 6. The actual shares of jobs reached in less than 30,45 and 60 min as functions of the total number of jobs in 40 U.S. cities in 2000.

10,000

10 -"<-1-

10 100 1,000 10,000

Total Number of Jobs in the Metropolitan Area

Fig. 5. The actual numbers of jobs reached in less than 30,45 and 60 min as functions of the total number of jobs in 40 U.S. cities in 2000.

Fig. 5 shows that the observed number of jobs within a 60-minute commute range increased systematically—by 97%, 3% short of 100%, to be exact—in a city with double the number of jobs in our sample of 40 U.S. cities; that the observed number of jobs within a 45-minute commute range increased by 94%, 6% short of 100%, in a city with double the number of jobs; and that the observed number of jobs within a 30-minute commute range increased by 87%, 13% short of 100%, in a city with double the number of jobs. In the 40 U.S. cities studied, the power functions representing these relationships all fit the observed data with an R2 of 0.99.5 This must be interpreted to mean that in cities with twice the numbers of jobs, the number of jobs accessed within a tolerable commute range increased by a fixed multiple, almost doubling the number of jobs accessed within that range.

To take a specific example: In 2000, the New York metropolitan area had 7.6 million jobs, twice the 3.9 million jobs in the Chicago metropolitan area. New York provided 85% more jobs that were reached in less than 60 min than Chicago did (6.2 vs. 3.6 million); 83% more jobs that were reached in less than 45 min than Chicago did (5.3 vs. 2.9 million); and 82% more jobs that were reached in less than 30 min than Chicago did (3.7 vs. 2.0 million). We must conclude, therefore, that the added friction created by the need to commute further and for a longer time in larger cities did compromise the size of their metropolitan labor markets, but only to a very minimal extent. The size of the metropolitan labor market—defined as the observed number of jobs that could be reached within a given time—almost doubled in cities with double the number of jobs or, more generally, with double the population.

The fact that the size of the metropolitan labor market almost doubled, but did not exactly double in a city with twice the workforce as a smaller one, must be examined in more detail by looking at the share of jobs in a metropolitan area that was reached within a given tolerable commute range. If that share were to stay fixed regardless of city size, then the size of metropolitan labor markets would exactly double in a city with twice the population or workforce. Examining the commuting data for the 40 U.S. cities in our sample in 2000, we found that this share declined slowly but steadily when city populations or, more specifically their workforces, increased in size. The relationship between the share of jobs that could be reached within a given tolerable commute time and the total number of jobs in the city is shown in Fig. 6. It shows that the observed share of jobs within a 60-minute commute range declined systematically—by 1%, to be exact—in cities with double the number of jobs; that the observed share of jobs within a 45-minute commute range declined by 3% in cities with double the number of jobs; and that the observed share of jobs within a 30-minute commute range declined by 7% in cities with double the number of jobs. The power functions fitted to the data still had excellent statistical fit—their R2 values in the range of 0.50-0.75—suggesting that the observed share of jobs reached within a given tolerable commute range declined slowly yet systematically with the total number of jobs in the city.6

Again, to take a specific example: In 2000, the Los Angeles area had 4.9 million jobs, 8 times the number of jobs in the Sacramento metropolitan area, 0.62 million. In Sacramento, 94% of all jobs were reached

5 The power function shown in Fig. 5 for the number ofjobs with a less than 60-minute commute, N60, as a function of the number of jobs in the metropolitan area, J, is N60 = 1.23J098 (R = 0.99), so thatN60(2J) = 1.97Ng0(J); for less than a 45-minute commute it is N45 = 1.61J095 (R = 0.99), so that N45(2J) = 1.94N4s(J); and for less than a 30-minute commute it is N30 = 2.75J089 (R = 0.99), so that N30(2J) = 1.86N30(J).

6 The power function shown in Fig. 6 for the share of jobs with a less than 60-minute commute, S60, as a function of the number of jobs in the metropolitan area, J, is S60 = 1.23J-0 021 (R = 0.50), so that S60(2J) = 0.99S60(J); for less than a 45-minute commute it is S45 = 1.611-0 046 (R = 0.60), so that S4s(2J) = 0.97S45CI); and for less than a 30-minute commute it is S30 = 2.75J-0106 (R = 0.75), so that S30(2J) = 0.93S30(J).

1 / 1.4142

Fig. 7. Distances between corresponding pairs of points increase in length by, or by 1.41, in two cities with the same shape with the right one double in area.

in less than 60 min, compared to 90% in Los Angeles; 88% of all jobs in Sacramento were reached in less than 45 min, compared to 81% Los Angeles; and 67% of all jobs in Sacramento were reached in less than 30 min, compared to 58% in Los Angeles. In a large metropolitan area like Los Angeles, therefore, nine-tenths of the total jobs were reached in less than 60 min, and three-fifths were reached in less than 30 min. We must conclude, therefore, that the added friction created by the need to commute further and longer in larger cities did compromise, to some extent, the potential size of their metropolitan labor markets. Indeed, the relative size of the metropolitan labor market—defined as the share of jobs that could be reached within a given time—declined systematically but the number of jobs in its labor market practically doubled in cities with twice the population of smaller ones.

These robust findings should dispel the concerns often voiced by urban economists that larger cities lose their productive advantage because of the added costs of long commuting trips along congested street networks. They demonstrate that even in the largest U.S. cities, the great majority of the workforce commuted for less than 60 min in 2000, and that in a city with a workforce twice the size of a smaller one, the metropolitan labor market—measured by the number of workers that actually reached their workplaces in less than 60 min, 45 min or 30 min—almost doubled in size as well.

3. Commuting time and city size

The aim of this section is to introduce evidence from our stratified sample of 40 U.S. metropolitan areas in the year 2000 that shows that in a city with twice the population of a smaller one, the actual increase in average commuting time is only one-sixth the expected increase. In general, other things being equal, commuting time in the larger city should be expected to increase by a factor of 2 as we shall explain below, in other words, by 41%. The observed increase, as we shall see, is only 7%. This is due to the three compounded adjustments or changes that take place in larger cities: densification, residential and workplace relocation that keep commuting times within tolerable commute ranges, and greater traffic mobility.

3.1. The square root of 2: the expected increase in average commuting time in a city with twice the population of a smaller one

When comparing two cities with the same average population densities, the same average commuting speeds, and one with twice the population of the other, what would be the expected increase in the average commuting time in the larger city?

Let us assume that there are two cities, one with twice the population of the other. We also assume that both workers' residences and their workplaces are uniformly distributed throughout their urban areas; that the average residential density is the same in both cities;

100 1,000 10,000 City Area (km2)

Fig. 8. Average distance between two random locations in the city as a function of city area in a sample of 40 U.S. metropolitan areas in 2000.

and that workers commute in straight lines and at equal speeds. It is easy to see that in two cities with the same non-circular shape where one has twice the area of the other, distances between any pair of corresponding points increase by the same factor, \/2, when the area of that shape doubles (see Fig. 7). The average of all those distances will, therefore, also increase by the same factor, V2, as well. More generally, if commuters travel at equal speeds and job and residential densities are the same everywhere, average commuting time increases by a factor of y/F when the population of a perfectly decentralized city of any given shape increases by a factor F while its shape remains the same.

Let us now look at the average distance between any two points in two perfectly decentralized cities of different shapes, where the area of one is twice the area of another. In these cities both residences and jobs are distributed evenly throughout the urban area. We graphed the average beeline distance between a random sample of point locations in every city against the area of that city in our stratified sample of 40 U.S. cities in 2000 (see Fig. 8). We found that in a city with twice the area of a smaller one, that average distance between random locations increased by a factor of 1.38 i.e. within 3% of V2. The relationship between the average distance between random points and the area of cities in the sample was systematic and robust (R2 = 0.91).7 Again, we can conclude that if commuters traveled at equal speeds and both residential and job densities were uniform everywhere, average commuting time between all locations in the city would be expected to increase by a factor of V2 (or by 41%) in a city with twice the population of another one even if their shapes were not the same. In reality, we found that in our stratified sample of 40 U.S. cities in 2000, the actual average commuting time in a city with twice the population of a smaller one increased, as expected, but it increased by a much smaller factor than V2. The question is why.

3.2. Larger U.S. cities are denser than smaller ones

Examining a stratified sample of 40 U.S. cities and metropolitan areas in 2000, we found that the area of a city with a population twice that of a smaller one was only 70% larger than that of the smaller city. This is illustrated in Fig. 9. The data is fitted with the power function, as before. According to this power function, the city area increased, on average, by only 70% in a city with twice the population of a smaller

7 The power function shown in Fig. 7 for the average distance between two random points Dr, as a function of the city area, A, is DR = 0.82A047 (R = 0.91), so that Dr(2A) = 1.38Dr(A).

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one. As the graph shows, the relationship between the area of a city and its population is very robust (R2 = 0.94).

Fig. 10 explains why the area of a city did not double in a city with twice the population of a smaller one. It shows the relationship between the average population density in the city and its total population in our sample of 40 U.S. cities in 2000. Again, the data is fitted with a power function. According to this power function, population density increased, on average, by 18% in a city with twice the population of a smaller one (R2 = 0.60). If this were the case, it can easily be shown that its area would increase by a factor F =1.7, namely by only 70% rather than by 100%.8 Other things being equal, if the area of a city increases only by a factor of 1.7, then—as we saw before—the average commuting distance in the city should increase by a factor of VTT7 = 1.3, namely only by 30% rather than by 41%.9 In other words, the higher density of larger cities in the U.S. brings their residences and workplaces into closer proximity and thus significantly reduces the average commuting distances among them: From the expected 41% in a city with twice the population of a smaller one to 30%.

3.3. Both workers and workplaces in larger U.S. cities move closer to each other to remain within an acceptable commute range

[L]ess newsworthy are the actions of the modest proportions of commuters who each year change residence and/or work place to avoid congestion and reduce their commuting times. These unsung heroes of metropolitan travel behavior explain why commuting times in the largest cities remain stable or decline despite impressionistic, but probably reliable, evidence of increasing congestion along particular highway segments (Gordon and Richardson 1991, 419).

Actual commuting distances in our sample of 40 U.S. cities— measured here as beeline distances between the centroid of a census tract containing a given commuter residence and the centroid of a

8 If the population is twice as large, P2 = 2Pi, and the density increases by 18%, D2 = 1.18D1, we should expect the area to increase by 70%, A2 = P2 / D2 = 2P1 /

1.18D1 = 1.7(P1 /D1) = 1.7A1.

9 The power function shown in Fig. 9 for the city Area, A, measured in square kilometers, as a function of the city population, P,isA = 0.029P076 (R = 0.94), so that A(2P) = 1.7A(P). The power function shown in Fig. 10 for the average population density in the city, D, measured in people per hectare, as a function of the city population, P, is D = 0.35P0 24 (R = 0.61), so that D(2P) = 1.18D(P).

census tract containing her workplace—increased, on average, only by 14% in a city with twice the population of a smaller one, slightly less than half the expected 30% increase as a result of densification. We ascribe this difference to the dynamic adaptation of metropolitan labor markets to increases in city size: The relocation of workers' homes to get closer to their actual jobs and the relocation of workplaces to get closer to their actual workers. In other words, in the larger city a worker will have to be closer to her own job than to all other jobs taken together than a worker in the smaller one; and workplaces will have to be closer to their workforce than to the entire metropolitan workforce. Or, put differently, a worker in the larger city will have to locate closer to her actual workplace—compromising her overall potential access to all other jobs in the city—than a worker in a smaller city; and a workplace in the larger city will have to locate closer to its actual workforce— compromising its overall potential access to the entire metropolitan labor pool—than a workplace in a smaller city.

We first discuss the relocation of workers to get closer to their workplaces. There is a considerable literature devoted to understanding the interdependence between residential location, job location, and commuting distance. A critical insight in this literature is that there is a tolerable commute range, a commuting radius, so to speak, within which workers are indifferent to distance or travel time 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 than those who change jobs to locations within it (Brown, 1975). As Clark, Huang and Withers note (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 and Kain, 1991). This is an important insight. It suggests that households have diverse reasons for moving from one location to another, and that moving closer to their workplace becomes critical only when the workplace is outside their tolerable commute range. Data from the U.S. Census Bureau for intra-county residential moves in 2008-2009 indeed confirms that only 8.9% of all residential moves were for employment-related reasons; that 5% of all those residential moves were to be closer to an existing workplace or to have an easier commute to that workplace; and that 2.1% were to be closer to a new workplace (see Table 1). We have reason to believe that most urban intra-county moves are within a single metropolitan area and that a substantial share of inter-county moves is also within a given metropolitan area. When we examine the data on inter-county moves for 2008-2009, we find that the longer the distance involved, the more important employment-related reasons become.

Fig. 11. Changes in distance to work after residential moves for 462 households in the Seattle, WA, area, 1989-1997.

Source: Calculated from Clark, Huang and Withers, 2003, Table 2, 207.

Namely, when jobs are outside a worker's tolerable commute range, she is more likely to move, and the further the job, the more likely she is to move: While the share of employment-related reasons for intra-county moves in 2008-2009 was only 8.9%, that share increases to 19.2% for inter-country moves of less than 50 miles, to 43.8% for inter-county moves of 50 to 199 miles, to 54.0% for moves of200-499 miles, and declined to 43.9% for inter-county moves of 500 miles or more (U.S. Census, 2011, Figure 4,17).

Clark, Huang and Withers (2003) provide empirical evidence pertaining to households that have changed residences—with or without changing their jobs—in the Seattle WA area between 1989 and 1997. They find that.

In the aggregate more households, whether with one or two workers, reduced their commutes after moving. Analyzing the results by the pre-move commute reveals a distinct pattern in which households with longer commutes before the move almost always reduced their commuting distance and time. (206-207)

Their findings are summarized in Fig. 11. The graph in Fig. 11 contains information on 462 households—some with one worker and some with two workers—that changed their residence during the study period, some while changing their jobs and some while retaining their jobs. As a group, a minority of 42% increased the distance of their commute when they relocated their homes, while a majority of 58% chose new residential locations that were either closer or at the same distance to their workplaces. But as the graph shows, the majority of commuters who lived less than 8 miles (12.8 km) from their workplace increased their commute distance when they moved. When their original distance to work was more than 16 miles (25.6 km), more than two-thirds of commuters moved to places that were closer to their jobs. And of those that originally lived more than 32 miles (51.2 km) away from their jobs, 95% found new homes in locations closer to their workplaces. We can draw a more general conclusion from this graph: Most commuters do not move closer to their workplaces as long as their workplaces are within a tolerable commute range, but they do move closer when their workplaces are outside their tolerable commute range.

In light of the findings in Table 1, the fact that workers do not seek to minimize their commute distance should come as no surprise: They have other reasons to guide their residential (and job) moves and they want to cast their net far and wide to find satisfactory locations,

be they for a home or for a workplace, subject to the constraint that, if at all possible, they should not be further from each other than their tolerable commute range. Indeed, the overall productivity of metropolitan labor markets does not require that workers be as close to their workplaces as possible, only that they be within a tolerable commute range of the best job they can find. And from the perspective of workers, that tolerable commute range should be quite generous because the larger and more varied the housing choices within their tolerable commute range of the best job they can find, the better off they will be. It stands to reason that it is these locational adjustments that keep the great majority of the urban workforce within its tolerable commute range regardless of how large the metropolitan area may be.

Having discussed the relocation of workers to get closer to their workplaces, we now turn to the discussion of the relocation of workplaces to get closer to their workforces. We first compare the Average Distance of Homes from the CBD10 with the Average Distance ofWork-places from the CBD in the 40 cities in our sample. The values for these metrics as a function of the areas of cities are displayed in Figs. 12 and 13. Fig. 12 reveals that in a city with twice the area of a smaller one, the actual average distance of commuter homes from the CBD increased by 35%.11 The increase was systematic and statistically significant (R2 = 0.87). Fig. 13 reveals that in a city with twice the area of a smaller one, the average distance of job locations from the CBD increased by 39%.12 This increase was systematic and statistically significant (R2 = 0.81) as well. The comparison of the two increases—35% and 39%—suggests that jobs are more decentralized than residences in larger cities than in smaller ones.

As we suspected, regardless of the size of cities, homes in American cities are more decentralized than jobs: The average distance of homes in our sample of 40 cities to the CBD in 2000 was 16.6 km, while the average distance of jobs to the CBD in the cities in the sample is 13.9 km and the two averages were significantly different from each other at the 95% confidence level. Because, as we noted above, jobs are more decentralized than commuter homes in larger cities than in smaller ones, we can surmise that in larger cities they are closer to homes, in relative terms, than in smaller ones. We can conclude, therefore, that in larger cities both workers and workplaces relocate to get closer to each other.

The literature regarding the question of whether the decentralization of jobs increased or decreased average commute distances is inconsistent. Some researchers (e.g. Aguilera, 2005; Cervero & Landis, 1991; Cervero & Wu, 1998; Levinson & Kumar, 1994; Naess & Sandberg, 1996; Parolin, 2005) find that decentralization increased both average commuting distances and average commuting times. Others (e.g. Giuliano, 1991; Giuliano & Small, 1993; Guth, Holz-Rau, & Maciolek, 2009) find that decentralization shortened average commuter distances. The evidence from our sample of40 cities is unequivocal. The average distance of homes to the CBD in these cities is 16.6 km, as noted above. This would be the average commute distance to jobs if all jobs were located in the CBD. But the observed average distance to jobs in our sample of cities is only 10.3 km, a distance significantly lower—indeed, less than two-thirds—than the hypothetical commute distance to the CBD if all jobs were concentrated there.13 We must

10 The average distance of home locations from the CBD in a given city is the sum of the product [number of commuter trip destinations in a census tract x the distance of census tract centroid from the CBD] for all tracts, divided by the total number of trip destinations in the city. The average distance of workplaces is calculated in a similar way.

11 The power function shown in Fig. 12 for the average distance of homes from the CBD, DH, measured in kilometers, as a function of the city area, A, measured in square kilometers, is Dh = 0.74A043 (R = 0.87), so that D„(2A) = 1.35D„(A).

12 The power function shown in Fig. 13 for the average distance of jobs from the CBD, Dj, measured in kilometers, as a function of the city area, A, measured in square kilometers, is Dj = 0.45A047 (R = 0.81), so that Dj(2A) = 1.39Dj(A).

13 Weighting these calculations by the number of commuters in each city in the sample

results in an average job distance from the CBD of 21.8 km and an average commuter home distance from the CBD of 25.2 km. The actual weighted average distance to a job in the cities in the sample is 13.0 km. Weighting increases the influence of cities with more commuters on the resulting averages.

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therefore conclude that by moving away from the CBD, workplaces have significantly shortened the commute distances of their employees. In fact, they shortened it, on average, by more than one-third.

As a result of the adjustments of both residence and workplace locations so as to be within a tolerable commuting range of each other, the observed average beeline distance between commuters' homes and their jobs in a city with twice the population of a smaller did not increase by 30%, the expected increase to its increased population density as we argued in the previous section. It increased only by 13%, less than half the expected increase due to increased population density, and this increase was most likely due to the relocation of workers and workplaces to get closer to each other. This is illustrated in Fig. 14, showing the average beeline commuting distance in a city plotted against its population. As the graph shows, this relationship is also very robust (R2 = 0.80).14 In short, larger cities compensate for the increase in their areas both by

Fig. 14. Average commuting distance as a function of city population in a sample of 40 U.S. cities in 2000.

increasing densities and by their workers and workplaces moving closer to each other, thus not compromising the size of their metropolitan labor markets and reaping the benefits of their higher productivity.

3.4. Greater mobility: commuters in larger cities travel at faster average speeds

The speed of an individual commuter on her way to work is the total distance covered by her trip—i.e. the sum total of the sidewalk, road, and rail segments she used—divided by the total time of her trip. The average commuting speed in a given city is thus the average speed of all its individual commuters. We were not able to obtain data on the actual distance traveled by individual commuters. But we did obtain data on the distribution of commuting times for commuters leaving a given census tract. We also obtained data on the share of commuters from that tract traveling to each census tract in the city, and thus on the distribution of beeline distances for all commuting trips leaving a given tract. We could thus calculate the average beeline speed for all commuting trips leaving a given tract, and the average beeline speed for all commuting trips in a given city as the weighted average of the average beeline commuting speeds from individual tracts. Although arrived at by separate calculations, the average commute time in a city is approximately equal to its average beeline distance divided by its average beeline speed. The average beeline speed can thus be construed as a simple measure of the overall mobility in the city, the ease with which the transportation system in the city allows its workers to reach their workplaces.

If we assume at the outset that, in a city with twice the population of a smaller one, average beeline speeds remain the same, then average commuting time in the larger city should increase by exactly the same proportion as the increase in average beeline distance, namely by 13%. If, for some reason, mobility in the larger city is impaired, commuting time should increase by more than 13% in a city with twice the population of a smaller one. Surprisingly, we find that in our sample of 40 U.S. cities in the year 2000, commuting time increased only by only by 7% in a city with twice the population of a smaller one, only half the expected increase of 13%. Fig. 15 shows the relationship between average commute time and city population in our stratified sample of 40 U.S. cities. As the graph shows, this relationship is very robust (R2 = 0.73).15

14 The power function shown in Fig. 13 for the average commute distance, D, measured in kilometers, as a function of the city population, P, is D = 0.79P018 (R = 0.80), so that D(2P) = 1.13D(P).

15 The power function shown in Fig. 15 for the average commute time, T, measured in

minutes, as a function of the city population, P, is T = 6.1P01 (R = 0.73), so that

T(2P) = 1.07T(P).

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Fig. 16. Average commuting speed as a function of city population in a sample of 40 U.S. cities in 2000.

The fact that commuting times increase at a slower rate than commuting distances suggests that larger cities offer greater mobility-reflected in faster commuting travel speeds—than smaller ones. Our data confirm that this is indeed the case. Fig. 16 displays the relationship between average commuting speed and city population. It shows that in a city with twice the population of a smaller one, average travel speed on the journey to work increased by 6%. The relationship is also robust (R2 = 0.38).16 What this figure makes clear, and quite surprising, is that our common perception—often repeated in economic analyses of urban agglomeration economies—that commuting in larger cities takes place at slower average speeds because of greater congestion on the roads appears to be wrong. Even though some roads in larger cities may be more congested, when looking at all commuting trips taken together, commuter travel in larger cities is not slower, but faster, on average, than commuter travel in smaller ones.

16 The power function shown in Fig. 16 for the average commute speed, V, measured in

kilometers per hour, as a function of the city population, P, is V = 7.7P0083 (R = 0.38), so that V(2P) = 1.06 V(P).

Fig. 17. In a square city, the arterial grid quadruples in total length when city area quadruples.

Part of the explanation for the ability of larger cities to keep congestion penalties at bay is that transportation infrastructure and traffic management in larger cities appears to keep up with their population growth and the expansion of their built-up areas. Road capacity in particular—and more specifically, the number of lane kilometers of freeways and arterial roads—increases sufficiently to accommodate the additional commuter traffic generated in larger cities by their larger populations commuting for longer distances.

What is the expected increase in arterial road kilometers, for example, to maintain the same road density (number of lane kilometers per square kilometer of area) when a city area doubles? Fig. 17 (left) shows a square city 10-by-10 km in area and a total area of 100 km2, with a grid of arterial roads, spaced 1-kilometer apart. The total length of the grid is 200 km and, therefore, road density is 2 km-per-km2. Now imagine a square city 20-by-20 km in area and a total area of 400 km2, with an arterial grid also spaced 1-kilometer apart (Fig. 17, right). It can be easily ascertained that the total length of the grid is this city is 800 km and that, therefore, road density is 2 km-per-km2 as well. In this example, when city area quadrupled, the total length of arterial roads quadrupled as well. More generally, we can expect that when a city area doubles, for road density to remain the same, the total length of arterial roads must double as well. If the total length of arterial road lanes more than doubles—and the width of arterial roads does not change—then we can conclude that there are more arterial roads in the city and that they are spaced closer together, namely that road density increased.

Fig. 18. The number of lane kilometers of freeways and arterial roads as a function of city area in 106 U.S. cities in 2011.

Fig. 19. The number of lane kilometers of freeways and arterial roads as a function of city population in 106 U.S. cities in 2011.

Fig. 20. Peak period observed travel speeds per lane kilometer on freeways and arterial roads as a function of city population size in 106 U.S. cities in 2011.

Data for 106 U.S. cities in 2011 (Shrank, Eisele, & Lomax, 2012) confirms that the number of freeway and arterial road lane kilometers increases at a faster-than-expected rate when city area increases (Fig. 18). In a typical city with twice the area of a smaller one, for example, arterial road lane kilometers increased by a factor of 226% and freeway lane kilometers increased by 233%. Those increases were both statistically significant (R2 = 0.91 and R2 = 0.82 respectively).17

If freeway lane kilometers increased by 233% in a city with double the area of a smaller one, then freeway lane density increased by a factor of 1.16 (2.33/2 = 1.16), or by 16%. If we assume that freeways were not widened to include more lanes, this implies that the average distance between freeways declined by a factor of V1.16 = 1.08, i.e. by 8%, when city areas doubled. The total amount of lane kilometers of arterials roads increased by 226%, on average, in a city with twice the area of a smaller one, i.e. arterial road lane density increased by a factor of 1.13 (2.26/2), or by 13%. Again, if we assume that arterial roads were not widened either, this implies that the average distance between arterial roads declined by a factor of V1.13 = 1 06, i.e. by 6%, when city areas doubled. We also observe that the density of freeways increased at a faster rate than the density of arterial roads when city areas doubled. On the whole, therefore, we can say that transportation infrastructure capacity in U.S. cities—measured simply as the availability, or more precisely the density, of freeways and arterial roads—increased at a faster rate than the increase in city area, so that road capacity was more plentiful in cities with larger areas than in cities with smaller ones.

We must recall, however, that when city areas double, their population densities increase by a factor of 1.18 (Fig. 10), a factor that is larger than the factors by which the lane densities of freeways or arterial roads increase. We must conclude, therefore, that lane kilometers of freeways or arterials roads do not quite double in a city with twice the population than a smaller one. This is clearly observed in Fig. 19. The graph shows that, in a city with twice the population of a smaller one, lane kilometers of freeways increased by 92% and lane kilometers of arterial roads increased by 87%. Those increases were both statistically significant

17 The power function shown in Fig. 18 for total arterial road lane length, LA, measured in kilometers, as a function of the city area, A, measured in square kilometers, is La = 0.84A118 (R = 0.91), so that La(2A) = 2.26La(A). The power function for total freeway lane length, LF, measured in kilometers, as a function of the city area, A, is Lf = 0.22A122 (R = 0.82), so that Lf(2A) = 2.33LF(A).

(R2 = 0.82 and R2 = 0.91 respectively).18 That means that the amount of freeway lane kilometers per capita declined by a factor of 1.04 or by 4% in a city with twice the population of a smaller one. The corresponding decline of arterial road lane kilometers per capita was 7%. All in all, although road density in larger cities increased, it did not increase at a rapid enough rate to allow for the increase in population density. Hence, we can conclude that freeways and arterial roads in cities with larger populations served more people and thus carried more traffic and were likely to be more congested than roads in cities with smaller populations.

It is no wonder, therefore, that peak period observed travel speeds on freeways and arterial roads decline regularly, albeit very slowly, in cities with larger populations. This is illustrated with data on 101 U.S. cities in the 2012 Urban Mobility Report presented in Fig. 20. The graph shows that in a city with twice the population as a smaller one, peak period observed travel speeds on freeways declined by 2.3%, and on arterial roads by 1.5%.19 That said, speeds were still considerably higher on freeways than on arterial roads. The average freeway speed during peak periods in the cities studied was 91.7 ±1.1 km per hour, some 63% higher than the speed observed on arterial roads, 56.4 ±1.0 km per hour.

So why did we observe that overall commuting speeds in larger cities are faster? The reason that average commuting speeds in larger cities are faster than those in smaller ones can be explained by the shift from arterial road travel to freeway travel in larger cities. This is illustrated in Fig. 21. As the figure shows, in a city with twice the population as a smaller one, the daily vehicle kilometers per lane kilometer of freeway increased by 13%, while that of arterial roads increased by only 5%.20 In other words, freeways carried a larger share of traffic at faster speeds.

18 The power function shown in Fig. 19 for total arterial road lane length, LA, measured in kilometers, as a function of the city population, P, is LA = 0.0114P09 (R = 0.91), so that La(2P) = 1.87La(P). The power function for total freeway lane length, LF, measured in kilometers, as a function of the city population, P, is LF = 0.025P094 (R = 0.82), so that Lf(2P) = 1.92Lf(P).

19 The power function shown in Fig. 20 for the peak period observed travel speed on freeways, VF, measured in kilometers per hour, as a function of the city population, P, is Vf = 146.5P-0 034 (R = 0.23), so that Vf(2P) = 0.977Vf(P). The power function for the peak period observed travel speed on arterial roads, VA, measured in kilometers per hour, as a function of the city population, P, is VA = 76.2P-0022 (R = 0.06), so that Va(2P) = 0.985Va(P).

20 The power function shown in Fig. 21 for daily vehicles per lane kilometer on freeways, KF, as a function of the city population, P, is KF = 722.1P017 (R = 0.46), so that Kf(2P) = 1.13KF(P). The power function for daily vehicles per lane kilometer on arterial roads, KA, as a function of the city population, P, is KA = 1175.2P0068 (R = 0.11), so that Ka(2P) = 1.05Ka(P).

Fig. 21. Observed daily vehicle per lane kilometer on freeways and arterial roads as functions of city population size in 106 U.S. cities in 2011.

5.8, (where 41 ^ 7 = 5.8).

(5) This factor of 5.8 is a product of three factors. Densification contributed a factor of 1.4; relocation contributed a factor of 2.3; and greater mobility contributed a factor of 1.9, where 1.4 x 2.3 x 1.9 = 5.8.

(6) This allows us to rank the three factors as well: Relocation contributed 1.6 times more than densification and 1.2 times more than greater mobility to the decrease in average commute time; greater mobility contributed 1.3 times more than densifica-tion to the decrease in average travel time.

(7) In percentage terms, we can say that densification contributed 25%, or one quarter, of the reduction in actual travel time from the expected travel time in a city with twice the population of a smaller one; relocation contributed 41% of that reduction; and greater mobility contributed 34%, or one third, of that reduction.

(8) This less-than-expected increase in commute time in larger cities is the key reason why metropolitan labor markets in American cities were able to grow almost in direct proportion to their population, as we saw earlier, and that is why larger American cities were able maintain their larger metropolitan labor markets and their higher productivity despite their great expanse, their large populations, and the more intense congestion on their roads.

More generally, we can say that in cities with larger populations, roads that are further up in the transport hierarchy carry a larger share of commuter traffic, and they carry it at faster speeds. A smaller share of trips use slower local and arterial roads and a higher share of trips uses the faster freeways. It is for this reason that we observed earlier that the overall average speed of commuter trips increased by 6% in a city in our sample with twice the population of a smaller one.

3.5. Section summary and remarks

To summarize this entire section, in our analysis of a stratified sample of 40 U.S. metropolitan areas in 2000 and of associated traffic data from 2011 we found that

(1) First, average population density in a city twice the size as a smaller one increased, on average, by 18%. As a result, its urbanized areas did not double; it increased only by 70%. Therefore, the average commuting distance—expected to increase by a factor of V2, or by 41%, in a city with twice the area of a smaller one—increased only by a factor of \/T7 = 1.3, namely by 30% instead of by 41%. In other words, densification decreased the expected average travel time by a factor of 1.4, or (1.41—1)/(1.3— 1) = 1.4.

(2) Second, in a city with twice the population of a smaller one, observed average commuting distance increased by only 13%, rather than by an expected 30%—because homes and workplaces throughout the metropolitan area relocated to get within an acceptable commute range of each other. In other words, relocation decreased the expected average travel time by a factor of 2.3, or (1.3-1)/(1.13-1) = 2.3.

(3) Third, in a city with twice the population of a smaller one, average commuting speeds increased by an average of 7%, rather than the expected 13%, as a result of greater mobility. In other words, greater mobility decreased the expected average travel time by a factor of 1.9, or (1.13-1) / (1.07-1) = 1.9.

(4) The cumulative result of these three adjustments—densification, relocation, and greater mobility—was that average commute time in a city with twice the population of a smaller one rose, on average, only by 7% instead of increasing by the expected 41% when city populations doubled. In other words, the actual increase in average commute time was only 17% of the expected increase, (where 7 ^ 41 = 17%), or smaller than expected by a factor of

In closing, we must note that much of the commuting data we used was for the year 2000 and that fifteen years have passed since that time. Following decades of decreasing average densities in U.S. cities, there has been a gradual increase in average densities in many U.S. cities in recent years. During the intervening time, both homes and jobs may have continued to decentralize, both away from the Central Business District (CBD) and away from employment sub-centers with possible effects on the average distance between homes and residences. There may have been parallel movements away from distant suburbs and into urban centers and sub-centers. There may also have been an increase in the number of two-commuter households, an increase that may have affected relocation patterns and thus the reduction in travel times due to relocation. There may also have been a shift in the preferences of households to live closer or further away from their homes, as well as changes in the overall levels of residential mobility. There may have been a significant increase in the number of people working at home or in their neighborhood, at least part of the time. Finally, there have been significant changes in car ownership patterns, in the ability of new transportation investments to keep up with increased demand, in the use of public transport, and in walking and bicycling, all of which may have had important effects on overall mobility in American cities. Surely, all of these factors may have important effects on the results of this work. Indeed, we do have plans to repeat this analysis with 2015 data, and this may enable us to examine these changes and their effects on commute time in greater detail. That said, we suspect that the results presented in this paper are indeed robust and that we expect to find only minor changes using more recent data, changes that are not likely to be radical enough to reverse our main findings.

4. Conclusion: the policy implications of the study

Urban transportation and land use planners and policy makers who are committed to fostering and maintaining the productivity of large metropolitan areas in the United States need to focus on facilitating commuting travel in the metropolitan area as a whole. Why? Because one of the most important economic advantages of a metropolitan area—if not its most important one—is the size of its labor market or, more precisely, the overall access of its labor to the jobs it offers: the access of firms to the largest possible pool of workers and the access of workers to the largest possible pool ofjobs. Not its overall mobility necessarily, but the overall mobility of its productive labor. Commuting may take up slightly more than one-quarter of all personal vehicle

Fig. 22. Locations of the 40 cities in the sample.

miles traveled (data for 2009, AASHTO, 2013, Table 2.1,9), but it is that quarter which drives the metropolitan economy.

To the extent that policy makers respond to the demand for metro-wide distribution of housing so that the great majority of commuters can find homes within a tolerable commute range of the best jobs they can obtain, to the extent that the respond to the metro-wide demand for business locations where this demand manifests itself, and to the extent that they respond to the demand for metro-wide travel where it is needed to get commuters from their actual residences to their actual workplaces quickly and cheaply, to that extent they indeed help metropolitan labor markets become more efficient and more equitable, and to that extent they make cities more productive. To the extent that they prevent or hinder workers from finding affordable homes within their tolerable commute range to the best jobs they can find throughout the metropolitan area, to the extent that they prevent or hinder businesses from locating within tolerable commuting range of their actual and potential workers, and to the extent that they readily provide speedy transportation where it is not needed while failing to provide it where it is needed, to the extent that they discourage long distance travel and favor short distance travel, to that extent they hinder and damage the performance of metropolitan labor markets, compromising their productivity, and impeding the economic performance of metropolitan areas.

Acknowledgments

We are indebted to Alain Bertaud for insisting that urban transport policy and land use planning focus on metropolitan labor markets, and to Geoffrey West, Luis Bettencourt, and José Lobo for introducing us to scaling phenomena in cities—the regular variation of key urban phenomena with city population size. These two critical insights form the

intellectual foundation of this work. Special thanks are due to Gregory Ingram for his detailed constructive comments on the manuscript.

Appendix Annex A. A stratified sample of 40 U.S. urbanized areas

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. 22. Their names, three letter labels, populations and areas, and are given in Table 2.

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