Agglomeration economies are a persistent subject of debate in regional science and city planning. Their definition turns on whether or not larger cities are more efficient than smaller ones. Here, we complement existing discussions on agglomeration economies by providing a sensitivity analysis of estimated externalities to the definitions of urban agglomeration. We regress wages versus population and jobs over thousands of different definitions of cities in France, based on an algorithmic aggregation of spatial units. We also search for evidence of larger inequalities in larger cities. This paper therefore focuses on the spatial and economic complexity of the mechanisms defining agglomeration within and between cities.@en

Both theoretical and empirical studies have shown the ability of scaling laws to reveal processes of emergence in urban systems. Nevertheless, a controversy about the robustness of results obtained with these models on empirical cases remains, regarding for instance the definition of the ‘city’ considered or the way the estimations are performed. Another source of bias is highlighted in this contribution, with respect to the non-ubiquitous character of some urban attributes (i.e. their partial absence from several cities of the system). The problem with the zero count for cities where these attributes are absent is that the technical necessities of usual estimation procedures make the analysis ignore them altogether even when they represent some valid information. This could seriously impact the results. A precise exploration of the effects of this arbitrary filtering is conducted here, and several solutions are proposed to overcome this limitation. In a case study about foreign investment towards French cities, we show that some erroneous conclusions about a hierarchical diffusion could be drawn when adopting the classical ordinary least squares approach. The framework we suggest specifies how it is possible to avoid misinterpretations deriving from the exclusion of zero values by using methods of analysis which deal with zero values specifically. The conclusion of a diffusion of foreign investment in the French urban system is then rejected.@en