Angeles, New Orleans, New York, Philadelphia, the San Francisco Bay Area, and St. Louis.<sup>55</sup> Depending on the exact methodology used, the exact number of sub‐centers varies but, in general all studies agree on multiple sub‐centers for a relatively large city.<sup>56</sup> For instance, the city of Los Angeles is found to have 41 sub‐centers when the more flexible non parametric technique of relying on the local maxima of each candidate sub‐center is used while there are 48 sub‐centers using the “10–10” definition and 10 sub‐ centers using the “20–20” thresholds for density and total employment in the clustering method.<sup>57</sup> In contrast, some small cities such as Austin in Texas, Buffalo in New York and Nashville in Tennessee do not have any sub‐centers at all.<sup>58</sup> Similar evidence exists for cities in other developed countries such as Barcelona or other metro cities in Spain as well as Paris in France. Even in the case of a developing country, large cities such as Bogota (Colombia), has evolved to generate 10 sub‐centers.<sup>59</sup> Besides the monocentric and polycentric models, recent advances in urban economics propose three other theoretical forms of spatial organization of cities. (i) Maximum Disorder model, where workers’ homes and their jobs are randomly distributed in the city. (ii) The Constrained Dispersal model, where a small number of sub‐centers exist outside the CBD and attract workplaces to each other or to shared public infrastructure and amenities. In this form, both workers and firms adjust their locations to remain within a tolerable commuting range of each other. (iii) The Mosaic of Live‐Work Communities, where workers and firms are all within walking or bicycling distance of each other. Of the 40 American cities examined in a recent study, evidence suggests that an average of 25% of jobs is located in sub‐centers and CBD while the remaining 75% are scattered throughout metropolitan areas. This suggests that while the polycentric model dominates over the monocentric one, it is the constrained dispersal model that appropriately describes the urban spatial structure among American cities.<sup>60</sup>

# **_Structural Changes with Urban Spatial Evolution: From Manufacturing to Tradable Services_**

As urban spatial structures have evolved from a monocentric organization to that of multiple centers of economic activity, so has the structural composition of the CBD. Since the World War II, manufacturing activity is de‐concentrating while services are increasingly agglomerating in central locations.<sup>61</sup> Research

> 55 Anderson and Bogart (2001) identify subcenters in Cleveland (9 sub centers), Indianapolis (11), Portland (11) and St. Louis (10); Bogart and Ferry (1999)  also study Cleveland and found 9 subcenters; Cervero and Wu (1997, 1998) analyze the San Francisco Bay Area; Giuliano and Small (1991) identify 35 subcenters, Redfearn (2007a) study Los Angeles and found 41 subcenters in 2000; and McMillen and McDonald (1998) identify 15 subcenters in the Chicago metropolitan area. McMillen (2001a) identifies 13 subcenters in Chicago, and reasonable subcenters in Dallas, Houston, Los Angeles, New Orleans, and San Francisco. This analysis is extended in McMillen and Smith (2003) to cities such as Atlanta (4 subcenters), Baltimore (5) Washington DC (10), Boston (11), New York (38), and Philadelphia (4). Others have focused on identifying points of peak density and estimating density gradients to formally test for polycentricity, for example, Small and Song (1994) for Los Angeles and Craig and Ng (2001) for Houston. 56 For example, using non‐parametric technique, Redfearn (2007a) finds 7 subcenters in orange county of Los Angeles city. Although the number of subcenters in Los Angeles county of the city is 28, orange county itself is also polycentric. 57 See Redfearn (2007a) and Giuliano et al. (2007)

> 58 McMillen and Smith (2003)

> 59 See Garcia‐López (2010a, 2010b), Holl and Viladecans‐Marsal (2011) Duarte et al. (2011), Mu ̃niz et al. (2008) for ci�es (particularly Barcelona) in Spain; Gilli (2005) for Paris in France; Avendaño and Enríquez (2012) for Bogota in Colombia; 60 See Angel and Blei (2015a)

> 61 Dumais et al. (2002), Kim (1995). Kolko (1999) finds that there has been a growing concentration of manufacturing in small and medium‐sized cities and of business services in larger cities.

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