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- approaches to the concept of urban hierarchy
- hierarchical trajectories
The notion of a hierarchy among cities has long been part of the theoretical tool kit of urban sociologists, geographers, and economists. Reviewing the evolution of the urban hierarchy concept, this paper empirically demonstrates a hypothesized transition in the U.S. urban hierarchy during the twentieth century, from size based to network based. Three urban types, following distinct trajectories during this shift, are explored: the primate city, the offline metropolis, and the wired town. Data on the economic structure, population size, and airline passenger traffic of 64 U.S. metropolitan areas from 1900 to 2000 are used to test the hypothesis of a hierarchical transition. Results suggest that a size-based hierarchy dominated in the early twentieth century but was replaced or augmented in the mid-1940s with a network-based hierarchy. The paper concludes with a discussion of the study's limitations and directions for future research.
De los lugares centrales a las redes: La transición en la jerarquía urbana de los Estados Unidos desde 1900 hasta el 2000 (Zachary P. Neal)
La noción de jerarquía urbana ha sido utilizada por mucho tiempo como parte del instrumental teórico de la sociología urbana, la geografía y la economía. Este artículo demuestra empíricamente la transición ocurrida en la jerarquía urbana de los Estados Unidos durante el siglo XX en que se pasó de una jerarquía basada en el tamaño de las ciudades a otra basada en las redes. Se abordan tres tipos urbanos que siguieron trayectorias distintas durante dicha transición: el modelo de primacía urbana, el modelo de la metrópolis autónoma y el modelo de la ciudad conectada. Para comprobar esta hipótesis de una transición en el tipo de jerarquía urbana, se hace uso de datos sobre estructura económica, población y tráfico aéreo de pasajeros de 64 áreas metropolitanas estadounidenses en el período 1900 – 2000. Los resultados indican que la jerarquía urbana basada en el tamaño fue el modelo dominante a principios del siglo XX pero fue reemplazada o aumentada a mediados de los años 40 con una jerarquía basada en redes. La conclusión del artículo incluye una discusión de las limitaciones del estudio y posibilidades para investigaciones futuras.
The notion of an urban hierarchy has long been part of the theoretical tool kit of urban sociologists, geographers, and economists. In some cases, the hierarchy is little more than a ranking of cities used to demonstrate the regularity of population distributions (e.g., Zipf, 1941), while in other cases it is used to explain functional differentiation (e.g., Duncan et al., 1960) or integration into the web of globalization (e.g., Alderson and Beckfield, 2004). The rankings invoked in such cases often enjoy significant face validity, placing highly visible and obviously dominant places at the top; there is the traditional American triumvirate of New York, Chicago, and Los Angeles (Abu-Lughod, 1999), while London and Tokyo are invariably included in global hierarchies (Sassen, 1991). However, the urban features used to empirically situate cities within such hierarchies have varied widely across studies (Beaverstock, Taylor, and Smith, 1999), and often do not mirror theoretical underpinnings, leading to ambiguity about the basis of cities’ status in urban hierarchies.
This paper seeks to resolve this ambiguity by addressing the hypothesis that the urban features structuring the U.S. urban hierarchy changed during the twentieth century. At the beginning of the twentieth century, many urban economies in the United States depended primarily on factors located within the city and its adjacent hinterland, thus situating cities in a size-based hierarchy like that described by central place theory. However, by the end of the twentieth century, technological innovations and economic restructuring led urban economies to depend more on factors located between cities, namely, the relationships among cities that permit the exchange of key resources and allow the development of interurban cooperation and economies of scale. This transition implies the emergence of a newer, more network-based hierarchy in which the dominant cities at the top of the hierarchy are those which serve as “basing points” for resources flowing through intercity networks (Friedmann, 1986).
Claims that urban networks and relations of interdependence structure urban systems (McKenzie, 1933) and shed new light on central place systems are certainly not new (Vance, 1970), and others have hypothesized just such a transition. Rimmer (1998), for example, has argued that “population is a misleading guide to identifying and determining the prospects and status of … cities. Attention has to shift from population to focusing on the accessibility of key nodes … in networks and on the degree of interactivity between them” (p. 466; c.f. Camagni, 1993; Meijers, 2007; Pumain, 1992). However, while many have theorized the importance of urban networks, relatively few have directly examined their influence. Thus, this analysis closes a significant evidential gap in the literature by examining the influence of both size-based and network-based urban hierarchies during a sufficiently wide time frame—the entire twentieth century—to make this hypothesized transition visible.
This paper is organized in five sections. The first section reviews prior theoretical and empirical work on urban hierarchies, highlighting the longstanding theoretical role that urban networks have played, but noting that the empirical incorporation of these ideas has been more gradual. The second section considers how a transition from a size-based hierarchy to one rooted in networks has manifested itself in the hierarchical trajectories of three urban types: the primate city, the offline metropolis, and the wired town. The third section describes the use of data on airline passenger traffic and industrial employment data from the Integrated Public Use Microdata Series (IPUMS) to measure the hierarchical status of 64 U.S. metropolitan areas in each decade from 1900 to 2000. The fourth section presents the results from a series of regression models designed to test the changing influence of size- and network-based urban hierarchies. Findings support the hypothesis that the factors underlying the structure of the U.S. urban hierarchy have changed, while further exploratory analyses suggest that such changes may proceed in waves. The paper concludes with a discussion of the consequences of adopting an air traffic-based picture of the urban network, the actual extent of the observed transition, and the potential for sector-specific effects.
approaches to the concept of urban hierarchy
- Top of page
- approaches to the concept of urban hierarchy
- hierarchical trajectories
Variations on central place models (e.g., Christaller, 1933; Lösch, 1954) have dominated research on functional urban hierarchies, where position in the hierarchy is associated with a city's economic functions within the urban system. Such models begin with the assumption that a city exists to provide goods and services for a surrounding tributary area within which it is located at the center, thus serving as a “central place” for commerce. Paralleling Smith's ( 2000) claim that the division of labor is limited by the extent of the market, the size of a city's tributary area determines the complexity of goods and services the city provides. Cities with large tributary areas offer the widest range of goods and services, from those satisfying the routine needs of nearby residents (e.g., groceries, personal banking) to specialized products (e.g., designer fashion, investment banking) for which there is more limited demand and consumers are willing to travel greater distances. In contrast, cities with smaller tributary areas offer a more limited range of products to a smaller consumer base within a smaller geographic territory. The extensiveness of a city's tributary area depends on its location relative to other cities along transportation routes that facilitate the movement and aggregation of consumers and goods. Thus, urban functions are organized hierarchically by cities’ centrality or importance within a region.
Although in theory central place models recognized the importance of urban networks and interdependence, in practice few studies directly examined such relational factors (e.g., Garrison, 1960), focusing instead on population size as a proxy indicator of centrality. That is, in many empirical investigations of central place hierarchies, larger cities were assumed to have larger tributary areas and were found to offer more complex goods and services (Berry and Garrison, 1958a). Thus, while central place models in their purest theoretical form hypothesized a network-based urban hierarchy, the majority of empirical applications hypothesized instead a size-based urban hierarchy (Preston, 1971). Adopting this stylized form of central place theory, marketers (e.g., Reilly, 1929), geographers (e.g., Berry and Garrison, 1958b), and sociologists (e.g., Schettler, 1943) amassed a large body of evidence suggesting that urban functions were organized according to a size-based urban hierarchy. Although this size-based conception of the urban hierarchy has received extensive attention and empirical support (see Berry and Pred, 1965; Mulligan, 1984, for reviews), it has also been critiqued for ignoring the role of networks highlighted by earlier forms of central place theory. Indeed, even Christaller recognized that indicators of intercity networks of exchange (e.g., telephones) should be preferred to attributes such as population size as measures of central place status (Ullman, 1941).
Urban ecology represented one of the earliest returns to an explicitly relational approach to urban hierarchies. By viewing cities as having complex relationships of interdependence with one another, much like living organisms, it sought to move beyond simple top-down relations of central place to hinterland where large cities dominate small ones. As McKenzie formulated the metropolitan dominance perspective, mirroring the central hypothesis of this paper, “centers and routes are gaining precedence over boundaries and political areas as points of interest in spatial distribution” (1927:28). He pointed to technological innovations in transportation as the catalyst and to a principle of competitive exclusion as the causal mechanism underlying this shift, noting that “the general contraction of space, the increasing fluidity of products and people … have the effect of intensifying intercity competition and [therefore] of bringing about various forms of intercity and interregional division of labor” (1933:158). These ideas were refined and empirically tested by Duncan and colleagues, who found an urban division of labor wherein occupations (e.g., Duncan and Reiss, 1956) and industries (e.g., Duncan et al., 1960) were sorted among cities based on their larger roles in an interdependent urban system: integration and coordination versus production and extraction. Notably, however, although McKenzie's and Duncan's conceptions of urban hierarchy explicitly drew on notions of interdependence and urban networks, empirical investigations tended to rely on nonnetwork indicators such as population size (Duncan and Reiss, 1956; Duncan et al., 1960; Winsborough, 1959, 1960). Thus, as with central place models, although in theory interurban relationships were recognized as critical, in practice they did not appear in empirical accounts of the urban hierarchy.
From a slightly different angle, the size-based conception of urban hierarchy was also critiqued by Vance (1970), who saw the central place model as useful only for closed, self-sufficient (i.e., endogenic) urban systems like those that emerged under feudalism. When advances in transportation technology facilitate the spatial separation of production and consumption activities, commerce in the form of wholesaling arises, which he argued cannot be explained by a purely spatial model. That is, while a size-based urban hierarchy may be able to explain “where the farmer goes in his Saturday marketing,” it cannot “account for the destination of his hogs” (Vance, 1970:162). To solve this deficiency, he proposed a mercantile model wherein dominant cities (i.e., those at the top of the hierarchy) emerge along natural and built transportation routes and derive their economic functions from the long-distance, inter-regional trading relationships these routes facilitate. Within this network of trade and transportation, subordinate cities then fill in the gaps following a central place-like pattern, with their economic functions derived from intra-regional exchange with the more dominant hubs. Empirical work has provided support for these ideas, demonstrating that since the late eighteenth century major U.S. cities have been integrated into an urban hierarchy structured by networks of information (Pred, 1973), transportation (Conzen, 1975a), capital (Conzen, 1975b), and bank correspondents (Conzen, 1977).
Despite minor theoretical differences in the metropolitan dominance (McKenzie, 1927, 1933) and mercantile (Vance, 1970) perspectives, both agreed that size-based central place models offer an incomplete understanding of how cities acquire their unique economic roles. While a size-based urban hierarchy may explain the distribution of some urban functions (e.g., retail goods and services), it says little about the distribution of other urban functions (e.g., trade or finance) that depend on long-distance interaction. Thus, their critique of central place theory did not propose the replacement of a size-based urban hierarchy with a network-based one, but rather their simultaneous operation, with each organizing different domains of urban economic activity. However, while size- and network-based urban hierarchies may both structure urban activity, as urban economies come to be disproportionately characterized by such activities as trade and finance, the network-based urban hierarchy may nonetheless hold greater explanatory power. Thus, these theories suggest a shift from size- to network-based hierarchy for key cities on major transportation routes (e.g., New York on the Atlantic ocean, New Orleans on the Mississippi river, Chicago on the railroad) as early as the 1790s, but for the majority of the U.S. urban system in the early twentieth century. Although others have empirically examined these revisions to central place theory, because they focused on major U.S. cities in the pretwentieth century (Pred, 1973; Conzen, 1975a, b, 1977) or conflated population size with status in a network-based hierarchy (Duncan and Reiss, 1956; Duncan et al., 1960), ambiguity about such a transition remains.
Although the advances in transportation and communication technology identified by metropolitan dominance and mercantile theories as responsible for a transformation of the U.S. urban hierarchy continue, a more recent series of economic changes have spurred new waves of research that also suggest an emerging network-based urban hierarchy. The development of a “new economy,” spurred by the growing importance of financial capital (Sassen, 1991) and a shift toward distance-independent activities such as business services (Esparza and Krmenec, 1994), has further diminished the role of space and location in structuring the urban hierarchy and defining cities’ economic roles and increasingly focused researchers’ attention on urban networks. As a result, a more explicit use of intercity networks emerged in explanations of the functional urban hierarchy's contours. For example, Lincoln (1978) and Ross (1987) found that U.S. cities’ centrality in a command and control network of headquarters-subsidiary linkages predicted the presence of higher order functions, while others found relationships between urban functional differentiation and U.S. cities’ positions in networks of trade (Eberstein and Frisbie, 1982; Eberstein and Galle, 1984), banking (Meyer, 1984), information diffusion (Mitchelson and Wheeler, 1994; Wheeler and Mitchelson, 1989), and transportation (Irwin and Kasarda, 1991; Ivy, Fik, and Malecki, 1995; Neal, 2010).
The burgeoning field of globalization and world cities research further extended support for a network-based urban hierarchy under conditions of internationalizing markets. Friedmann and Wolff (1982) defined world cities as those places at the apex of an urban hierarchy of influence whose “determining characteristic is not their size of population,” as had been the case with the earlier size-based hierarchy, but rather the extent of their integration “with the global system of economic relations” (p. 310). Similarly, Castells (1996) identified two contrasting ways that social and economic activity is organized: a “space of places” in which a locale's function derives from characteristics contained within its boundaries and a “space of flows” in which a locale's function emerges from its connections to other locales. Drawing on these ideas, much attention has been focused on the hierarchies implied by the world city network, using data on airline traffic (Smith and Timberlake, 2001), multinational headquarters and subsidiaries (Alderson and Beckfield, 2004), and corporate service firms (Neal, 2008). Work in this area is ongoing, but preliminarily suggests the continuing importance of a network-based urban hierarchy into the twenty-first century.
Table 1 summarizes the theoretical and empirical evolution of the urban hierarchy concept. Scanning down the second column, it is clear that the core theoretical propositions of each perspective on urban hierarchy rest on the critical role of urban networks and relations of interdependence. From the earliest central place models to the recent work on world cities, scholars have theorized that cities’ positions within an urban hierarchy depend on networks. However, scanning down the third column, it is also clear that these theoretical propositions have not always translated into empirical practice. In the central place and metropolitan dominance models, although the role of networks is highlighted in theory, in practice cities’ population size was more often identified as a key factor around which urban hierarchies were organized. More recently, however, studies have offered evidence that directly supports both new and old theorizing about the role of networks. Thus, as Table 1 illustrates, while twentieth century research was characterized by theoretical consistency in conceptions of networks structuring an urban hierarchy, it was also characterized by empirical change in the measurement and evidence for those claims.
Table 1. Theoretical and Empirical Evolution of the Urban Hierarchy
|Perspective||In Theory …||In Empirical Practice …|
|Central place (Christaller, 1933)||Urban functions are organized hierarchically by the extensiveness of cities’ tributary areas, which depend on cities’ location along transportation routes.||Population size is used as a proxy indicator for tributary area size. Urban functions are organized hierarchically by city size (e.g., Schettler, 1943).|| |
|Metropolitan dominance (McKenzie, 1927, 1933)||Urban functions are organized by cities’ interdependent relationships, made possible by new transportation and communication technology.||Population size is used as a proxy indicator for dominance in relations of interdependence. Urban functions are organized hierarchically by city size (e.g., Winsborough, 1959).|| |
|Mercantile (Vance, 1970)||A size-based hierarchy organizes some functions (e.g., retail), while a network-based hierarchy organizes others that depend on long-distance interaction (e.g., wholesale).||Confirmed for large cities before the twentieth century through direct analysis of urban transportation networks (e.g., Pred, 1973).|| |
|New economy (Sassen, 1991)||Urban functions depend more on networks than size because urban economies are increasingly focused on distance-independent activities (e.g., finance and business services).||Observed in the late twentieth century for multiple urban networks: corporate (Lincoln, 1978), trade (Eberstein and Frisbie, 1982), information (Wheeler and Mitchelson, 1989), transportation (Irwin and Kasarda, 1991).|| |
|Globalization (Castells, 1996)||The emergence of “world cities” as basing points in the flow of global capital heightens the importance of relational factors for urban function.||Observed in the late twentieth and early twenty-first centuries (Smith and Timberlake, 2001; Alderson and Beckfield, 2004), but investigation is ongoing and hampered by data availability.|| |
This pattern suggests that the factors structuring the U.S. urban hierarchy have transitioned. To be sure, this review and the discussion that follows do not describe a dramatic epochal shift from one urban hierarchy to another, but rather a gradual evolution in the way scholars have thought about and measured the factors that underlie urban hierarchies since the beginning of the twentieth century. The following sections trace this evolution in a few specific cities, then in the twentieth century U.S. urban system.
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- approaches to the concept of urban hierarchy
- hierarchical trajectories
To empirically examine the three urban archetypes described above—the primate city, offline metropolis, and wired town—Figure 2 plots each city's rank in the size-based urban hierarchy in 1930 and in the network-based urban hierarchy in 2000. To contextualize these results without rendering the plot unreadable, only selected cities are labeled: all cities in the sample that are identified as exemplars in Table 2, as well as five additional cities (Denver, Grand Rapids, Phoenix, Spokane, and York). The dashed lines divide the space into quadrants corresponding to those in Table 2. Cities above the horizontal dashed line are the 15 most populous cities in 1900, occupying top positions in the early size-based urban hierarchy. Similarly, cities right of the vertical dashed line are the 15 most connected cities in 2000, occupying top positions in the emerging network-based urban hierarchy.
Most cities in this sample occupy lower positions in both hierarchies (i.e., the unnamed lower left quadrant) and have played only minor roles in coordinating the urban system (e.g., York, PA; Grand Rapids, MI; Spokane, WA). However, clear groupings among some cities are apparent. Primate cities like New York, Chicago, and Los Angeles were large and influential early in the twentieth century but continue to be influential through their connectivity. Offline metropoli like Pittsburgh and Cleveland, while initially large and influential as industrial centers, have not maintained equally high positions in the newer network-based hierarchy. Instead, their positions of influence have been assumed by such smaller but better-connected wired towns like Miami, as well as young cities that have experienced explosive growth in their interurban connections (e.g., Denver, Phoenix). While primarily descriptive, this plot generally supports the face validity of the hierarchical trajectories and corresponding urban archetypes articulated in Table 2 and the associated discussion above. Notably, although Detroit is characterized above as an offline metropolis, it appears here in the quadrant corresponding to the primate city type. This (mis-) classification is likely driven by the use of an airline traffic network to define cities’ status in the network-based hierarchy. As one of Delta Airlines’ hubs, Detroit's network-based status is artificially inflated due to the large volume of connecting passengers. This apparent centrality is driven by largely by spatial factors like the city's convenient location in the middle of the country but does not indicate the presence of extra-regional ties because such connecting passengers are in Detroit (or rather, it is outskirts) for only an hour or so and contribute little if anything to the city itself. This potential source of bias when using airline traffic data is considered below in the discussion section and has been examined in greater detail by Neal (2010).
Turning to the two hypotheses offered in the previous section, what effect does a city's position in these two hierarchies have on its economic structure, and has this effect changed over the past century? Notably, these hypotheses are nested: H1 posits that in a given decade ECONOMY is related to SIZE and NETWORK, while H2 posits that the strength of the relationships described by H1 vary over time. Therefore, the procedure used to evaluate these hypotheses follows a similarly nested design like that described by Blau and Alba (1982).7
To test hypothesis H1, the following ordinary least squares (OLS) regression model is estimated, separately for each decade from 1900 to 2000:
That is, cities’ economies are a function of their position in the size-based hierarchy (in all decades) and network-based hierarchy (since 1940). The straight-line distance (in miles) between each pair of cities is included to control for the likely influence of cities’ proximity on their economies, sizes, and air traffic levels. Because dyadic (i.e., city pair) observations are not independent, statistical significance is assessed using Mantel's (1967) nonparametric approach with 100,000 permutations. Despite an expectedly close association between SIZE and NETWORK (e.g., r = .79 in 1990), because the variance inflation factors (1.22 in 1940 to 3.23 in 2000) do not exceed ten (Gujarati, 2003) and because the nonparametric approach does not rely on standard errors to judge statistical significance, multicollinearity is not believed to be a problem. The estimates for each decade's regression are displayed in Table 4. All significant and nearly significant estimates are positive, providing support for hypothesis H1, that differences in two cities’ positions within an urban hierarchy are positively associated with dissimilarities in their economies.
Table 4. Estimates of Regressions Predicting Dissimilarity of Cities’ Economies, by Decade
|Year||Constant (α)||Size (β1)||Network (β2)||Distance (β3)|
To test hypothesis H2, two OLS regression models that treat the slopes in Equations (2) and (3) as functions of time are estimated:
The results, displayed in Figure 3 and reported in Table 5, demonstrate that over the twentieth century the strength of the size-based hierarchy's influence on cities’ economies significantly declined (γ1=−0.0004, p < 0.01), while at the same time the strength of the network-based hierarchy's influence significantly increased (γ1= 0.0003, p < 0.05). The intersection of these two regression lines provides support for H2, that a transition in the organization of the U.S. urban hierarchy occurred during the twentieth century. More specifically, while the U.S. urban system was once organized around a size-based hierarchy, it is now increasingly organized around a network-based hierarchy.
Table 5. Linear Model of Hierarchical Transition
|Size Slope (β1)||Network Slope (β1)|
|Year (γ)||−.0004 (.00006)**|| .0003 (.00007)*|
|Constant (α)|| .7878 (.11218)**||−.5414 (.13707)*|
waves of hierarchical transition?
The evidence of a transition from a size- to a network-based urban hierarchy is strong, but a purely linear model of this transition is theoretically problematic. First, such a model suggests that the size-based hierarchy once had, or that the network-based hierarchy will eventually have, a near-infinite influence over cities’ economies. Instead, it is more likely that specific forms of urban hierarchy grow, peak, then decline in influence. Second, it suggests that as earlier forms of the urban hierarchy decline in influence, they acquire a negative influence (e.g., the size-based hierarchy in Figure 3 after about 1970), which would imply that cities with different positions in the hierarchy have similar economies. Instead, it is more likely that obsolete forms of hierarchy simply decline into statistical nonsignificance. Together, these modifications suggest that a more reasonable model of this transition ought to be curvilinear (Batten and Thord, 1995; Berry, 1991).
To explore this possibility, Equations (4) and (5) are reestimated using STATA's nonlinear least squares command to predict each slope (β1 and β2) as a nonlinear function of time:
This function fits the data to a bell-shaped curve. Table 6 presents the coefficient estimates, while Figure 4 illustrates the curvilinear pattern of predicted slopes (i.e., level of influence of the two hierarchies on cities’ economies) during the twentieth century; dashed lines illustrating predictions for the preceding and following 50 years are included to highlight the curve's basic shape. Because the model's complexity and small sample sizes do not allow reliable estimates of standard errors or the assessment of the coefficients’ statistical significance, these values are not presented. However, for reasons discussed above, this functional form is more theoretically motivated than a simple linear model. Moreover, comparison of the nonlinear model's adjusted R2 values to those from the linear model indicates that it describes the size-based hierarchy transition equally well (adjusted R2= 0.84 [linear model] vs. 84 [nonlinear model]) and the network-based hierarchy transition better (adjusted R2= 0.76 [linear model] vs. 0.97 [nonlinear model]).
Table 6. Nonlinear Model of Hierarchical Transition
|Size Slope (β1)||Network Slope (β1)|
|σ|| 24.80|| 43.03|
|σ′|| 13.42|| 14.70|
Figure 3 in essence “zooms in” on the linear portion at the middle of Figure 4. However, the temporally expanded and more theoretically motivated view illustrated in Figure 4 may offer some, albeit heuristic, insights into the potential catalysts of a hierarchical transition. First, it raises the possibility that a size-based hierarchy may have been less influential before the mid-nineteenth century, at a time when locational (e.g., proximity to a waterway) or political (e.g., seats of government) factors may have been more important. Second, it locates the size-based hierarchy's peak influence just after the beginning of the twentieth century, which closely corresponds to the selection of Federal Reserve cities on the basis of population size and spatial dominance (Reserve Bank Organization Committee, 1914), in essence imposing an institutionalized size-based hierarchy upon the nation's financial system. Third, it suggests that the network-based hierarchy's greatest gains in influence occurred in the last quarter of the century, following the 1978 Airline Deregulation Act, which effectively eliminated a mandated central place-like hub-and-spoke structure and paved the way for a more complete point-to-point network of exchange. Finally, the projected late twentieth century decline of the network-based hierarchy's influence, while partly driven by right-censored data and the peculiarities of Equation (6), nonetheless raises interesting questions about the potential for transitions to other forms of urban hierarchy in the future.