URBAN SPATIAL STRUCTURE Alex Anas, Richard Arnott, and Kenneth A. Small May 1, 1998 JEL subject code: R1 Keywords: Spatial structure, land use, agglomeration, subcenters, polycentricity The authors are with the University of Buffalo, Boston College, and the University of California at Irvine, respectively. Acknowledgments: The authors would like to thank the editor, three referees, Robert Bacon, Amihai Glazer, Peter Gordon, Robert Johnston, Cassey Lee Hong Kim, and David Pines for helpful comments on earlier drafts, and Alexander Kalenik for assistance in the preparation of Figure 1. We also thank the University of California Transportation Center for financial assistance. I. Introduction An interview with Chicago's current mayor, Richard M. Daley: 'New York is too big this way,' the mayor says, raising a thick hand over his head. Stretching both arms out at his sides, he adds, 'Los Angeles is too big this way. All the other cities are too small. We're just right.' (Jeff Bailey and Calmetta Coleman 1996, p. 6) Mayor Daley's remarks reflect a widespread fascination with the roles that urban size and structure play in people's lives. Academic as well as other observers have long sought explanations for urban development patterns and criteria by which to judge their desirability. Furthermore, as we shall see, understanding the organization of cities yields insights into economy-wide growth processes and sheds light on economic concepts of long-standing interest: returns to scale, monopolistic competition, vertical integration, technological innovation, innovation diffusion, and international specialization. Cities also are prime illustrations of some newer academic interests such as complex structural evolution and self-organization. In this essay we offer a view of what economics can say about and learn from urban spatial structure. In doing so, we reach into neighboring disciplines, but we do not aspire to a complete survey even of urban economics, much less of the related fields of urban geography, urban planning, or regional science. Our focus is on describing and explaining urban spatial structure and its evolution. This is a particularly interesting time to study urban structure because cities' growth patterns are undergoing qualitative change.1 For two centuries at least, cities have been spreading out. But in recent decades this process of decentralization has taken a more polycentric form, with a number of concentrated employment centers making their mark on both employment and population distributions. Most of these centers are subsidiary to an older central business district (CBD), hence are called "subcenters." Some subcenters are older towns that gradually became incorporated into an expanded but coherent urban area. Others are newly spawned at nodes of a transportation network, often so far from the urban core as to earn the appellation "edge cities" (Joel Garreau 1991). There is some evidence, discussed later, that the employment centers within a given urban region form an 1Throughout this essay we use the word "city," or the name of a particular city, to mean an entire urban region; other terms with similar meanings are "metropolitan area" and "urban area." 1 interdependent system, with a size distribution and a pattern of specialization analogous to the system of cities in a larger regional or national economy. At the same time, rampant dispersion of economic activity has continued outside centers altogether, prompting Peter Gordon and Harry Richardson (1996) to proclaim that Los Angeles, at least, is "beyond polycentricity." But even sprawl is far from homogeneous, and geographers have perceived patterns that conform to the mathematics of highly irregular structures such as fractals. Whether such irregularity is really new, or even increasing, is not so clear, as we shall see in the next section; but urban economics helps us understand the order that may be hidden in such patterns. An important source of current change in urban structure is the changing economic relationships within and between firms. Telecommunications, information-intensive activities, deregulation, and global competition have all contributed to changes in the functions that firms do in-house, and in how those functions are spatially organized. Some internal interactions can now be handled via telecommunications with remote offices which already perform routine activities such as accounting. Some vertical interactions are now more advantageously made as external transactions among separate firms, possibly requiring even more frequent face-to-face communications because of the need for contracting. Allen Scott (1988, 1991) describes how such "vertical disintegration" has shaped the geographical structure of a number of industries in southern California including electronics, animated films, and women's clothing. Meanwhile, firms are developing new interactive modes which are neither market nor hierarchy but rather constitute what Walter Powell (1990) calls a "network" organizational form, characterized by "relationship contracting" and having unknown implications for locational propensities. The research agenda that emerges from these observations is heavy on economies of agglomeration, a term which refers to the decline in average cost as more production occurs within a specified geographical area. One class of agglomeration economies is intra-firm economies of scale and scope that take place at a single location. Another class is positive technological and pecuniary externalities that arise between economic agents in close spatial proximity2 due, for example, to knowledge spillovers, access to a common specialized labor pool, or economies of scale in producing intermediate goods. Agglomeration economies may be dynamic as well as static, and are suspected of 2Some authors reserve the term "agglomeration economies" only for this second class. 2 giving cities a key role in generating aggregate economic growth (Jane Jacobs 1984; Edward Glaeser et al. 1992). Any agglomerative or "centripetal" force, even one caused just by a unique resource such as a harbor, places a premium on land at certain locations. This encourages spatially concentrated capital formation (buildings) and accentuates the need to produce at discrete points in space because of increasing returns to scale in production (David Starrett 1974). Because of these pervasive externalities and nonconvexities, economic analysis when applied to urban geography yields results that differ in important and interesting ways from results of other branches of economics. Agglomeration economies also create first-mover advantages and regional specializations that are important in international trade (Paul Krugman 1991a), and some first-mover disadvantages that prevent optimal dynamic growth paths from being realized. We discuss these in Section V. Agglomeration economies are of course not new. As eloquently exposited by Raymond Vernon (1960) and Benjamin Chinitz (1961), they are at the heart of our current understanding of central business districts. But recent changes in the technology of agglomeration, due to advances in information processing and telecommunications, may profoundly alter the pattern of spatial development (Jess Gaspar and Glaeser 1998). Understanding these new forces will help us understand newly emerging forms of urban structure as well as basic determinants of industrial structure and interregional and international trade. While our focus is on explaining urban spatial structure as a result of market processes, we touch on two related issues as well. The first concerns the role of government. Government policy — notably land-use controls and the provision of transportation infrastructure — plays a major role in shaping cities. What can we say about optimal policy? The second issue concerns the importance of space in economics. Accounting for location yields new insights into economic phenomena that are normally analyzed in aspatial models. But what is the level of spatial resolution at which such phenomena are best analyzed? II. History and Description of Urban Spatial Structure 3 We begin with a sketch of how urban form has evolved in modern times, followed by some observations on how to measure its characteristics. A. Recent Evolution of Urban Form The spatial structure of modern cities was shaped, in large measure, by advances in transport and communication. The history of urban development in North America since colonial times allows us to document aspects of this process (Charles Glaab and Theodore Brown 1967). Prior to about 1840, most cities were tied to waterways such as harbors, rivers, and canals. The average cost of processing freight fell sharply with the quantity processed at a particular port, creating substantial scale economies at harbors or river junctions with access to the sea. Similarly, as railroads competed with waterways later in the 19th century, scale economies in rail terminals created accessibility advantages near them as well. Meanwhile intra-urban freight transport took place mainly by horse and wagon, which was time consuming and unreliable in bad weather. These conditions favored the growth of a single manufacturing district located near the harbor or railhead, with residences surrounding it (Leon Moses and Harold Williamson 1967). In the last quarter of the century, the telegraph greatly speeded the flow of information from city to city (Alexander Field 1992). But economies of scale prevented it from being used much within a city — instead, messengers remained the primary means of intra-city business communication. The high cost of intra-urban communication meant that even light manufacturing and service industries tended to concentrate within the central manufacturing core, as shown for New York by Chinitz (1960). But this small core area was far from homogeneous; rather it was divided into districts, each specialized in an activity such as commercial banking, pawnbrokerage, or light or heavy manufacturing. In late nineteenth-century Chicago, four-fifths of the city's jobs were located within four miles of State and Madison streets according to Raymond Fales and Moses (1972), who go on to show how a pattern of specialized districts arose due to agglomerative forces within industries and the linkages among them. Before 1850, personal transport within the city was mainly by foot and horse-drawn carriage, causing the great majority of rich and poor alike to live close to the city center. For the most part, the rich outbid the poor for the most central and hence most convenient sites, so that income declined 4 markedly with distance from the CBD as is documented in studies of Milwaukee, Pittsburgh, and Toronto (Stephen LeRoy and Jon Sonstelie 1983). Between 1850 and 1900, the advent of horse-drawn and then electric streetcars enabled large numbers of upper- and middle-income commuters to move further out. This migration gave rise to "streetcar suburbs," residential enclaves organized around a station on a radial streetcar line (Sam Warner 1962). Toward the turn of the century subways further contributed to this pattern in the largest cities. Thus developed a spatial structure now known as the "nineteenth century city," consisting of a compact production core surrounded by an apron of residences concentrated around mass transport spokes. The next big changes were the dissemination of the internal combustion engine and the telephone in the early twentieth century. Gradually the horse and wagon was replaced by the small urban truck, and the messenger by the telephone. For example, in the single decade from 1910 to 1920, truck registrations in Chicago increased from 800 to 23,000 while horse-drawn vehicle registrations dropped almost by half. Moses and Williamson (1967) estimate that variable costs and travel time for the truck were less than half those for the horse and wagon. The truck and the telephone allowed businesses to spread outward from the center, thereby taking advantage of lower land values while maintaining their links to the central port or railhead. Thus central business districts expanded. In Chicago, firms that moved in 1920 located on average 1.5 miles from the core, as opposed to 0.92 miles in 1908 (Moses and Williamson 1967). The automobile, at first restricted to richer families, rapidly increased in importance with assembly-line production of the Model T Ford starting in 1908. Cars broadened the coverage of motorized personal transport, causing the areas between the streetcar suburbs to be settled and the residential apron to expand. The automobile competed successfully with mass transit despite transit fares remaining flat in nominal terms from the beginning of the century until approximately World War II; it did this mainly by providing speed, privacy, and convenience although it was also facilitated by an active program of building and upgrading public roads (Paul Barrett 1983). As assembly-line production became widespread, the lower capital-land ratios characterized by flat buildings increased the attractiveness of locations where land was cheap. Nevertheless, even at mid-century many producers outside the core were bound to the central harbors and rail terminals for 5 inter-city shipments. Eventually, however, this link was weakened by the creation of suburban rail terminals and the declining cost of inter-city trucking, the latter facilitated by the interstate highway system. These developments, coming primarily after World War II, enabled manufacturing to leapfrog out to the outermost suburbs. Central cities began their painful transition from manufacturing to service and office centers. Due to the durability of the urban capital stock and urban infrastructure, cities in the modern American landscape bear proof of the lasting impacts of these developments. Large cities of the eastern seaboard and midwest, such as Boston or Detroit, still contain streets and buildings dating from the heyday of their harbor and rail operations, and from the subsequent era of radial mass transportation systems. Even Chicago, the great metropolis of the midwest, was first established as one of the last and western-most of the waterway cities — its later importance as a rail and air hub derived from its already well established position by the beginning of the rail era (William Cronon 1991). Further west, however, the spatial pattern of many urban settlements was first shaped by the railroad. Major cities such as Oklahoma City, Denver, Omaha, and Salt Lake City grew up around rail nodes and developed compact CBDs centered on rail terminals. In contrast, the even later automobile-era cities such as Dallas, Houston, and Phoenix have spatial structures determined mainly by the highway system. Los Angeles is an intermediate case: partly a western rail terminus and partly a set of residential communities populated by rail-based migration from the American midwest, its many towns became connected to each other by high-speed highways and eventually merged into one vast metropolis. The most recent phase is the growth of "edge cities" in the suburban and even the most outer reaches of large metropolitan areas, both old and new (Garreau 1991). An edge city is characterized by large concentrations of office and retail space, often in conjunction with other types of development, including residential, at the nodes of major express highways. Most are in locations where virtually no development, possibly excepting a small town, existed prior to 1960. In many cases the initial design and construction was the product of a single development company, even a single individual. Edge cities are made possible by ubiquitous automobile access, even when they are located at a transit station as occasionally happens.3 3The huge Walnut Creek office and retail complex 22 miles east of San Francisco, which developed in the 1970s and 1980s, has at its center a station of the Bay Area Rapid Transit system which opened in the early 6 Cities in western Europe have evolved somewhat differently. Being much older, many still have centers which started out as medieval towns. There is a greater mixture of residences and businesses in the core, possibly because of the rich cultural amenities there. Apartment buildings are more common and public transportation more important. Nevertheless, as in North American cities, there has been massive suburbanization and the emergence of edge cities. B. Describing Urban Structure Using basic land-use data, scholars have sought to describe the regularities and irregularities of urban structure. We are particularly interested in the degree of spatial concentration of urban population and employment. We distinguish between two types of spatial concentration. At the city- wide level, activity may be relatively centralized or decentralized depending on how concentrated it is near a central business district. The degree of centralization has been studied mainly by estimating monocentric density functions, and is discussed in Section III. At a more local level, activities may be clustered in a polycentric pattern or dispersed in a more regular pattern. It is this clustering that has captured the recent attention of both theoretical and empirical economists. Defining such clusters precisely, however, is not so easy. If one uses three-dimensional graphics to plot urban density across two-dimensional space, one is struck by how jagged the picture becomes at finer resolutions. An example is presented in Figure 1, which plots 1990 employment density in Los Angeles County (a portion of the Los Angeles urban region) using a single data set plotted at three different degrees of spatial averaging.4 A similar lesson from the fractal approach discussed below is that within a fixed area, development that appears relatively homogenous at a coarse scale may actually (..continued) 1970s. Yet, the automobile accounts for 95 percent of commuting trips to the complex, and presumably an even higher proportion of other trips (Robert Cervero and Kang-Li Wu 1998, Table 5). 4The data (available on request) are plotted on a 121 X 131 kilometer square locational grid, with a spatial smoothing function used to compute the smoothed average density at each grid point from the raw data for nearby zones. If zone i‘s centroid is distance D from the grid point, its density is weighted i proportionally to [1-(D/R)]2, where R is the smoothing radius within which zone densities are allowed to i affect a given grid point. In the three plots shown in the figure, R takes values equal to 2√2, 4√2, and 6√2 kilometers respectively. 7 contain a great deal of fine structure. Where fine structure is present, it becomes somewhat arbitrary to say how large a concentration of employment is required to define a location as a subcenter. Even an isolated medical office has a high employment density when viewed at the scale of the building footprint, but we would not call it a subcenter. What about a cluster of twenty medical offices? What if this cluster is adjacent to a hospital and a shopping center? The distinction between an organized system of subcenters and apparently unorganized urban sprawl depends very much on the spatial scale of observation. We consider three approaches to describing the fine structure of urban development. The first two are ways of mathematically describing distributions of points in space. The third is the basis for extensions of monocentric density functions to a polycentric pattern. The first approach, called point pattern analysis, defines various statistics involving distances between observed units of development (R.W. Thomas 1981). These statistics are then compared with theoretical distributions. One such comparison distribution is that resulting from perturbations of a regular lattice, such as is postulated by one variant of central place theory (Walter Christaller 1966) in which development occurs in a hierarchy of centers, each with a hexagonal market area. Another comparison distribution is that resulting from purely random location, which can be described as a Poisson process. An example of the use of point pattern analysis is the search for population clusters in the Chicago area by Arthur Getis (1983). A more recent approach to describing urban spatial patterns is based on the idea that they resemble fractals, geometric figures which display ever-finer structure when viewed at finer resolutions. Mathematically, a fractal is the limiting result of a process of repeatedly replicating, at smaller and smaller scales, the same geometric element. Thus the fractal has a similar shape no matter what scale is employed for viewing it. If the original element is one-dimensional, the fractal's length becomes infinite as one measures it at a finer and finer resolution; the classic example is a coastline. One plus the elasticity of measured length with respect to resolution is known as the fractal dimension. So for example a coastline might have length L when measured on a map that can just resolve 100-meter features, and Lx10D-1 when 10-meter features can be seen; its fractal dimension would then be D, at least within that resolution range. A perfectly straight coastline has fractal dimension one, since its length does not increase with the level of resolution. 8 Geographers have used fractals to examine the irregularity of the line marking the outer edge of urban development in a particular urban region. Michael Batty and Paul Longley (1994, pp. 174-179) use data on land development in Cardiff, Wales, to define such a boundary to an accuracy as fine as 11 meters. Their best estimates of the fractal dimension of this boundary are between 1.15 and 1.29. (By way of comparison, Britain's coastline has fractal dimension 1.25, Australia's 1.13.) Surprisingly, they find that the fractal dimension of Cardiff's outer edge of development declined slightly over the time period examined (1886 to 1922), a period of significant transport improvements, mainly in the form of streetcars. They conclude that "the traditional image of urban growth becoming more irregular as tentacles of development occur around transport lines is not borne out" (p. 185). More significantly, one can use fractals to represent two-dimensional development patterns, thereby capturing irregularity in the interior as well as at the boundary of the developed area. For example, a fractal can be generated mathematically by starting with a large filled-in square, then selectively deleting smaller and smaller squares so as to create self-similar patterns at smaller and smaller scales. Such a process simulates the existence of undeveloped land inside the urban boundary. The fractal dimension D for this situation can be measured by observing how rapidly the fraction of zones containing urban development falls as zonal size is decreased, i.e. as resolution becomes finer. (More precisely, D is twice the elasticity of the number of zones containing any development with respect to the total number of zones into which the fixed urban area is divided.) We call this dimension the areal fractal dimension; it can vary from 0, indicating that nearly all the interior space is empty when examined at a fine enough resolution, to 2, indicating that each coarsely-defined zone that contains development is in fact fully developed. Long narrow development would have D=1 (since as we increase the total number N of zones into which a well-defined region is divided, the number of zones containing any development would grow only as √N). Batty and Longley (1994, Table 7.1) report estimated areal fractal dimensions for many cities around the world, with the result most often in the range 1.55 to 1.85. For Paris in 1981 the estimate is 1.66. For Los Angeles in the same year, it is 1.93, tied with Beijing for the highest among the 28 cities reported. This latter estimate implies that the fraction of area developed is almost constant at different scales, indicating a relative absence of fine-structure irregularities in development patterns. Apparently Los Angeles has grown in a more homogeneous manner than Cardiff or Paris. 9