Directed or Undirected? A New Index to Check for Directionality of Relations in Socio-Economic Networks

This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to justify an undirected (respectively, directed) network analysis. We introduce a new index that satisfies two main properties. First, it can be applied to both binary or weighted graphs. Second, once suitably standardized, it distributes as a standard normal over all possible adjacency/weights matrices. To test the index in practice, we present an application that employs a set of well-known empirically-observed social and economic networks

Coordination, Local Interactions and Endogenous Neighborhood Formation

The paper presents a local interaction model of coordination with spatially-located agents who simultaneously choose stage-game strategies and adaptively learn how to choose their neighbors. We analyze the behavior of the system when network externalities become eventually negative as neighborhood sizes increase. We show that the society can robustly reach in the long-run steady states characterized by high levels of coordination and small average neighborhood sizes. Moreover, we find that: (i) neighborhood adjustment allows for higher coordination than if interaction structures were static; and: (ii) large populations attain higher coordination provided that average initial neighborhood sizes are not too small.Learning, Coordination, Nearest-Neighbor Interactions, Endogenous Neighborhood Formation.

A Note on Equilibrium Selection in Polya-Urn Coordination Games

We study equilibrium selection in coordination games played by a population whose size increases over time. In each time period, a new player enters the economy, observes current strategy shares and irreversibly chooses a strategy on the basis of expected payoffs. We employ a simple Polya-Urn scheme to discuss the efficiency of long-run equilibria under alternative individual decision rules (e.g. best-reply, logit, etc.). We show that the system delivers a predictable outcome only when agents employ either a linear or a logit probability rule. If agents employ deterministic best-reply rules, Pareto-efficient coordination can occur, but the actual outcome depends on initial conditions and chance. In all other cases, coexistence of strategies characterizes equilibrium configurations.Coordination Games, Equilibrium Selection, Pareto-Efficient vs. Risk- Dominant Equilibrium, Polya-Urn Schemes.

The International-Trade Network: Gravity Equations and Topological Properties

This paper begins to explore the determinants of the topological properties of the international - trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a ''residual'' ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and so on. We then compare the topological properties of the original and residual ITNs. We find that the residual ITN displays, unlike the original one, marked signatures of a complex system, and is characterized by a very different topological architecture. Whereas the original ITN is geographically clustered and organized around a few large-sized hubs, the residual ITN displays many small-sized but trade-oriented countries that, independently of their geographical position, either play the role of local hubs or attract large and rich countries in relatively complex trade-interaction patterns.International Trade Network; Gravity Equation; Weighted Network Analysis; Topological Properties; Econophysics

Modeling the International-Trade Network: A Gravity Approach

This paper investigates whether the gravity model (GM) can explain the statistical properties of the International Trade Network (ITN). We fit data on international-trade flows with a GM specification using alternative fitting techniques and we employ GM estimates to build a weighted predicted ITN, whose topological properties are compared to observed ones. Furthermore, we propose an estimation strategy to predict the binary ITN with a GM. We find that the GM successfully replicates the weighted-network structure of the ITN, only if one fixes its binary architecture equal to the observed one. Conversely, the GM performs very badly when asked to predict the presence of a link, or the level of the trade flow it carries, whenever the binary structure must be simultaneously estimated

Modeling the International-Trade Network: A Gravity Approach

This paper investigates whether the gravity model (GM) can explain the statistical properties of the International Trade Network (ITN). We fit data on international-trade flows with a GM specification using alternative fitting techniques and we employ GM estimates to build a weighted predicted ITN, whose topological properties are compared to observed ones. Furthermore, we propose an estimation strategy to predict the binary ITN with a GM. We find that the GM successfully replicates the weighted-network structure of the ITN, only if one fixes its binary architecture equal to the observed one. Conversely, the GM performs very badly when asked to predict the presence of a link, or the level of the trade flow it carries, whenever the binary structure must be simultaneously estimated.International Trade Network; Gravity Equation; Weighted Network Analysis; Topological Properties; Econophysics

Do Liquidity Constraints Matter in Explaining Firm Size and Growth? Some Evidence from the Italian Manufacturing Industry

The paper investigates whether liquidity constraints affect firm size and growth dynamics using a large longitudinal sample of Italian manufacturing firms. We run standard panel-data Gibrat regressions, suitably expanded to take into account liquidity constraints (proxied by cash flow). Moreover, we characterize the statistical properties of firms size, growth, age, and cash flow distributions. Pooled data show that: (i) liquidity constraints engender a negative, statistically significant, effect on growth once one controls for size; (ii) smaller and younger firms grow more (and experience more volatile growth patterns) after controlling for liquidity constraints; (iii) the stronger liquidity constraints, the more size negatively affects firm growth. We find that pooled size distributions depart from log-normality and growth rates are well approximated by fat-tailed, tent-shaped (Laplace) densities. We also study the evolution of growth-size distributions over time. Our exercises suggest that the strong negative impact of liquidity constraints on firm growth which was present in the pooled sample becomes ambiguous when one disaggregates across years. Finally, firms who were young and strongly liquidity-constrained at the beginning of the sample period grew persistently more than those who were old and weakly liquidity-constrained.Firm Size, Liquidity Constraints, Firm Growth, Investment, Gibrat Law

Minority Games, Local Interactions, and Endogenous Networks

In this paper we study a local version of the Minority Game where agents are placed on the nodes of a directed graph. Agents care about being in the minority of the group of agents they are currently linked to and employ myopic best-reply rules to choose their next-period state. We show that, in this benchmark case, the smaller the size of local networks, the larger long-run population-average payoffs. We then explore the collective behavior of the system when agents can: (i) assign weights to each link they hold and modify them over time in response to payoff signals; (ii) delete badly-performing links (i.e. opponents) and replace them with randomly chosen ones. Simulations suggest that, when agents are allowed to weight links but cannot delete/replace them, the system self-organizes into networked clusters which attain very high payoff values. These clustered configurations are not stable and can be easily disrupted, generating huge subsequent payoff drops. If however agents can (and are sufficiently willing to) discard badly performing connections, the system quickly converges to stable states where all agents get the highest payoff, independently of the size of the networks initially in place.Minority Games, Local Interactions, Endogenous Networks, Adaptive Agents