Gravity models of networks: Integrating maximum-entropy and econometric approaches

Vece, Marzio Di; Garlaschelli, Diego; Squartini, Tiziano

doi:10.1103/physrevresearch.4.033105

Cited by 5 publications

(14 citation statements)

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“…With this contribution, we refine the theoretical picture provided in a companion paper [18], introducing models to infer the topology and the weights of undirected networks defined by continuous-valued data. In order to do so, we present a theoretical, physics-inspired framework capable of accommodating both integrated and conditional, continuous models, our goal being threefold: 1) testing the performance of both classes of models on the WTW in order to understand which one is best suited for the task; 2) offering a principled derivation of currently available, conditional, econometric models; 3) enlarging the list of continuous-valued distributions to be used for econometric purposes.…”

Section: Introductionmentioning

confidence: 88%

“…Discrete maximum-entropy models can be derived by performing a constrained maximization of Shannon entropy [37][38][39]. However, unlike the companion paper [18], our focus, here, is on continuous probability distributions. In such a case, mathematical problems are known to affect the definition of Shannon entropy and the resulting inference procedure.…”

Section: Conditional Modelsmentioning

confidence: 99%

“…because of a limited trading capacity); the possibility of establishing a very small amount of trade (in fact, so small to be compatible with statistical noise and, as such, removed). A general drawback of employing ZI models is that of predicting sparser-thanobserved network structures [18]; moreover, only discrete distributions (specifically, either the Poisson or the negative-binomial one [19]) have been considered, so far, to carry out the proper weight-estimation step. Hurdle models, introduced to overcome the limitations affecting zero-inflated models, can predict zeros only at the first step [20]: in any case, the presence of links is established by employing either a logit or a probit estimation step.…”

Section: Introductionmentioning

confidence: 99%

“…The most prominent examples descend from the Maximum-Entropy Principle (MEP) [37][38][39] applied to network ensembles [21,22], prescribing to maximize Shannon entropy [23,24] in a constrained fashion to obtain the maximally unbiased distribution of networks compatible with a chosen set of structural constraints. This approach is formally equivalent to the construction of so-called Exponential Random Graphs (ERGs) for social network analysis [25] but differs in the typical choice of the constraints: in particular, when the enforced constraints are local, such as the degree (number of links) and the strength (total link weight) of each node, maximum-entropy network models have been shown to successfully replicate both the topology and the weights of many economic and financial networks, including the WTW [5,6,18,[26][27][28][29][30][31][32]. The entire framework can also accommodate possibly degenerate, discrete-valued, singleor multi-edges [33].…”

Section: Introductionmentioning

confidence: 99%

“…Although maximum-entropy models have been also studied from an economic perspective (see [34] for a discussion of the economic relevance of the constraints defining the Poisson and the geometric network models), it is only recently that progress has been made to reconcile the above two approaches, allowing for economic factors parametrizing the maximum-entropy probability distribution producing links and weights [5,6,18,[29][30][31][32] or by introducing network-related statistics into otherwise purely econometric models [35]. On one hand, the novel framework enriches the methods developed by network scientists with an econometric interpretation; on the other, it enlarges the list of candidate distributions usable for econometric purposes.…”

Section: Introductionmentioning

confidence: 99%

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Reconciling econometrics with continuous maximum-entropy models

Vece¹,

Garlaschelli²,

Squartini³

2022

Preprint

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In the study of economic networks, econometric approaches interpret the traditional Gravity Model specification as the expected link weight coming from a probability distribution whose functional form can be chosen arbitrarily, while statistical-physics approaches construct maximumentropy distributions of weighted graphs, constrained to satisfy a given set of measurable network properties. In a recent, companion paper, we integrated the two approaches and applied them to the World Trade Web, i.e. the network of international trade among world countries. While the companion paper dealt only with discrete-valued link weights, the present paper extends the theoretical framework to continuous-valued link weights. In particular, we construct two broad classes of maximum-entropy models, namely the integrated and the conditional ones, defined by different criteria to derive and combine the probabilistic rules for placing links and loading them with weights. In the integrated models, both rules follow from a single, constrained optimization of the continuous Kullback-Leibler divergence; in the conditional models, the two rules are disentangled and the functional form of the weight distribution follows from a conditional, optimization procedure. After deriving the general functional form of the two classes, we turn each of them into a proper family of econometric models via a suitable identification of the econometric function relating the corresponding, expected link weights to macroeconomic factors. After testing the two classes of models on World Trade Web data, we discuss their strengths and weaknesses.

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Section: Introductionmentioning

confidence: 88%

Section: Conditional Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reconciling econometrics with continuous maximum-entropy models

Vece¹,

Garlaschelli²,

Squartini³

2022

Preprint

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Commodity-specific triads in the Dutch inter-industry production network

Di Vece,

Pijpers,

Garlaschelli

2024

Sci Rep

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Triadic motifs are the smallest building blocks of higher-order interactions in complex networks and can be detected as over-occurrences with respect to null models with only pair-wise interactions. Recently, the motif structure of production networks has attracted attention in light of its possible role in the propagation of economic shocks. However, its characterization at the level of individual commodities is still poorly understood. Here we analyze both binary and weighted triadic motifs in the Dutch inter-industry production network disaggregated at the level of 187 commodity groups, which Statistics Netherlands reconstructed from National Accounts registers, surveys and known empirical data. We introduce appropriate null models that filter out node heterogeneity and the strong effects of link reciprocity and find that, while the aggregate network that overlays all products is characterized by a multitude of triadic motifs, most single-product layers feature no significant motif, and roughly 85% of the layers feature only two motifs or less. This result paves the way for identifying a simple ‘triadic fingerprint’ of each commodity and for reconstructing most product-specific networks from partial information in a pairwise fashion by controlling for their reciprocity structure. We discuss how these results can help statistical bureaus identify fine-grained information in structural analyses of interest for policymakers.

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Reconstructing supply networks

Mungo,

Brintrup,

Garlaschelli

et al. 2024

J. Phys. Complex.

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Network reconstruction is a well-developed sub-field of network science, but it has only recently been applied to production networks, where nodes are firms and edges represent customer-supplier relationships. We review the literature that has flourished to infer the topology of these networks by partial, aggregate, or indirect observation of the data. We discuss why this is an important endeavour, what needs to be reconstructed, what makes it different from other network reconstruction problems, and how different researchers have approached the problem. We conclude with a research agenda.

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Gravity models of networks: Integrating maximum-entropy and econometric approaches

Cited by 5 publications

References 64 publications

Reconciling econometrics with continuous maximum-entropy models

Reconciling econometrics with continuous maximum-entropy models

Commodity-specific triads in the Dutch inter-industry production network

Reconstructing supply networks

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