The literature of the World City network calls into question inherited Euclidian, Cartesian and Westphalian notions of geographical scale as a fixed, neutral and static platforms for the economic relations; and calls for a methodology that can overcome the chronic lack of relation data and that allows to depict the timeframe, the evolution, the topological properties and the spatial structure of the network.
The research aims to contribute to the literature by developing a dynamic graphical model for non- stationary time series, or, in other words, a network analysis for long-run relationships.
The research assumes that the structure of the network is made of cliques, i.e., set of nodes all connected with each other, and treats the network directly as an unobservable variable.
The methodology is based on the unobserved component (UC) model developed by Harvey (1989), which disentangles the series into two components, denominated trend (long-run component) and cycle (short-run component). The trend component and the cycle component are both composed by a common term among the variables and by an idiosyncratic term specific to each series. The common terms are interpreted as network: a long-run network in the case of the trend component and a short-run network in the case of the cycle.
Time-varying technique allows these unobserved variables to change over time and smooth transition prior is imposed on their temporal variation to ease the problem of data scarcity.
The model, combining relational and evolutionary perspective together, will provides new insight on the functioning, the timing and the structure of the World City network.
The aim is contribute to the literature by developing a dynamic graphical model for cointegrated time series, or, in other words, a network analysis for long-run relationships. Indeed, despite the increase attention to network in time series analysis, there has been no advancement to model and interpret network for non stationary series.
This extension has been motivated by the literature of the World City network, which calls into question inherited Euclidian, Cartesian and Westphalian notions of geographical scale as a fixed, neutral and static platforms for the economic relations; and calls for a methodology that can overcome the chronic lack of relation data and that allows to depict the timeframe, the evolution, the topological properties and the spatial structure of the network.
The proposed methodology is capable to combine the relational and evolutionary approach to quantify the World City network.
The need for the relational approach can be find in Ben Deruder's (2006) statement "this enduring quest for relational data stems from the observation that, in a networked context, important cities derive their status from what flows between them rather than from what remains fixed within them".
The model can be improved by set the dimensionality of the trend and cycle components to be grater than one. In this case, each element of the components is interpreted as a clique, i.e., a set of nodes all of them connected with each other. If variables are allowed to be in more than a clique, some of them play the role of separator variable, which, despite of the name, have meaningful economic interpretation as gateway of interdependencies.
By confronting the magnitude of the loading coefficient with the idiosyncratic term is possible to make an evaluation of the strength of the connection to the network for each series, i.e., can be interpret as a measure of participation to the network. On the other hand by comparing the loading coefficient of the different cliques the analysis provides an hierarchy in term of participation to the different cliques, for each series and for the overall World City Network. Moreover it identifies which cities allows the connection among different cliques, i.e., which cities are the gateways among different parts of the networks, and thus, it defines its structure and its topological properties.
To understand the meaning of the clique the analysis proposes to use the covariates suggested in the literature, that can help to identify the clique and the type of neighbour for each city. It will be possible to identify geographical cliques, institutional cliques or organizational cliques, and with the evaluation of their loading coefficients, this will yield more insight on the structure and the functionality of the network.