Gravity Models of Networks

Trade networks are mathematical representations of the ex- changes established by countries, industries, firms or individ- uals. The present thesis collects works aimed at overcoming the limitations characterizing the econometric recipes tradi- tionally employed to study the aforementioned systems, by introducing a novel framework, based upon the maximum- entropy formalism. In chapter 2 we develop a novel class of models to study networks with discrete weights, capable of accommodating both structural and econometric parameters, finding that they outperform standard, econometric models [1]. In chapter 3 we extend the aforementioned set of models to study networks with continuous weights [2]. In chapter 4 we go beyond the ‘deterministic’ optimization procedure pre- scribed by econometrics to specify conditional models, con- sidering two, alternative estimation recipes characterized by different ways of averaging over the topological randomness: what we find is that the ‘annealed’ recipe, prescribing to max- imize a generalized likelihood function, is to be preferred, re- gardless of the heterogeneity of weights [3]. Finally, in Chap- ter 5, we delve into the extent to which the triadic structures embedded within the Dutch multi-commodity production net- work align with maximum-entropy conditional models [4]. Our findings reveal that for the vast majority of commodities, these models effectively replicate the observed triadic struc- tures, exhibiting minimal deviations.