Analysis and reconstruction of production networks

The economy is an ecosystem of firms, lenders, and consumers that can only be understood by studying the interaction between the agents that compose it. Firms, heterogeneous in nature and size, constitute a central component of the system. The supply chains that they establish, their organizational structure, and the innovation that they adopt ultimately determine the allocation of resources, employment levels, opportunities for investment, and what goods are produced. As such, production networks lie at the heart of economic analysis as they allow us to represent the superposition of the numerous supply chains that constitute the core of the economic ecosystem. A production network is therefore a photograph of the current configuration of productive activity. Unfortunately most macroeconomic analysis must rely on industrial aggregates as data on individual firms’ relationships is not widely available and is generally subject to privacy concerns. Information on firms’ input-output relationships are often private and it is therefore difficult to build a granular representation of direct interaction between businesses. For most applications this might be sufficient, however it is expected that, when the system undergoes substantial change, being able to realistically model the heterogeneous nature of firms and their relationships will be crucial to accurately predict future evolutions of the system.    In this thesis we attempt to provide a sound methodology for reconstructing inter-firm relationships when only partial information is available. This is a crucial contribution in order to be able to complement macroeconomic analysis with realistic network structures for firms when such information is not public. In particular we develop two methodologies: the first is rooted in a constrained maximum entropy ensemble that preserves the mesoscopic production structure of an economy; while the second is based on a principle of scale-invariance which is key to be able to handle consistently data across different levels of aggregation. Both methods are then tested for their ability to reconstruct accurately some important network features of the real empirical network constructed from client to client payments of two large Dutch financial institutions. Our results show that both methodologies are suitable to be used in order to create a probability distribution over the space of all graphs that contain the true observed one and preserve key topological properties. Finally we analyse some temporal properties of the empirical network with a particular focus on link persistence with the intent of trying to characterize how firms respond to changes to their environment. Overall this thesis aims at providing suitable methods to understand the static and dynamic properties of production networks and proposes several approaches to generate synthetic graphs that share many properties with real production networks.