Conventional studies of bilateral trade patterns specify a log-normal gravity equation for empirical estimation. However, the log-normal gravity equation suffers from three problems: the

Empirical research establishing the costs and benefits that can be associated with polycentric urban systems is often called for but rather thin on the ground. In part, this is due to the persistence of what appear to be two analytically distinct approaches in understanding and measuring polycentricity: a morphological approach centring on nodal features and a functional approach focused on the relations between centres. Informed by the oft-overlooked but rich heritage of urban systems research, this paper presents a general theoretical framework that links both approaches and discusses the way both can be measured and compared in a coherent manner. Using the Netherlands as a test case, it is demonstrated that most regions tend to be more morphologically polycentric than functionally polycentric. The difference is largely explained by the size, external connectivity and degree of self-sufficiency of a region’s principal centre.

Recent concepts as megaregions and polycentric urban regions emphasize that external economies are not confined to a single urban core, but shared among a collection of close-by and linked cities. However, empirical analyses of agglomeration and agglomeration externalities so-far neglects the multicentric spatial organization of agglomeration and the possibility of 'sharing' or 'borrowing' of size between cities. This paper takes up this empirical challenge by analyzing how different spatial structures, in particular the monocentricity -polycentricity dimension, affect the economic performance of U.S. metropolitan areas. OLS and 2SLS models explaining labor productivity show that spatial structure matters. Polycentricity is associated with higher labor productivity. This appears to justify suggestions that, compared to relatively monocentric metropolitan areas, agglomeration diseconomies remain relatively limited in the more polycentric metropolitan areas, while agglomeration externalities are indeed to some extent shared among the cities in such an area. However, it was also found that a network of geographically proximate smaller cities cannot provide a substitute for the urbanization externalities of a single large city. Free AbstractRecent concepts as megaregions and polycentric urban regions emphasize that external economies are not confined to a single urban core, but shared among a collection of close-by and linked cities. However, empirical analyses of agglomeration and agglomeration externalities so-far neglects the multicentric spatial organization of agglomeration and the possibility of 'sharing' or 'borrowing' of size between cities. This paper takes up this empirical challenge by analyzing how different spatial structures, in particular the monocentricity -polycentricity dimension, affect the economic performance of U.S. metropolitan areas. OLS and 2SLS models explaining labor productivity show that spatial structure matters. Polycentricity is associated with higher labor productivity. This appears to justify suggestions that, compared to relatively monocentric metropolitan areas, agglomeration diseconomies remain relatively limited in the more polycentric metropolitan areas, while agglomeration externalities are indeed to some extent shared among the cities in such an area. However, it was also found that a network of geographically proximate smaller cities cannot provide a substitute for the urbanization externalities of a single large city.

The current dynamics in the Western European urban system are in marked contrast with the bourgeoning literature stressing the importance of agglomeration for economic growth. This paper explores whether this is due to the rise of 'city network economies', leading to processes of borrowed size as well as the rise of agglomeration shadows in networks of cities. The spread of metropolitan functions over Western European cities is analysed. It is found that network connectivity positively enhances the presence of metropolitan functions, but local size remains the most significant determinant for most types of functions. The importance of size and network connectivity differs across metropolitan functions and across cities.JEL classification: R12, R11

Abstract'Borrowed size' is an emerging policy concept in several European countries, presenting theoretical potential to explain contemporary urban dynamics unaddressed through conventional urban growth theories that emphasise the role of agglomeration economies. In its original conceptualisation by Alonso, the concept describes and explains the situation that especially smaller cities that are located in a larger 'megapolitan complex' do perform better because they have access to agglomeration benefits of larger neighbouring cities. This paper scrutinises the concept of borrowed size, thereby focusing on its conceptualisation and reviewing its empirical justification thus far. Our empirical analyses show that the concept must be stretched in terms of scale and scope to enhance its policy value. Borrowed size occurs when a city possesses urban functions and/or performance levels normally associated with larger cities. This is enabled through interactions in networks of cities across multiple spatial scales. These networks serve as a substitute for the benefits of agglomeration.Theoretically, the borrowed size concept demands a recasting of the geographical foundations of agglomeration theory.

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