arXiv subjects

José Moran

Publications and source records attributed to José Moran.

14 recordsLinked to original sources

arXiv2026

Resilient-to-Fragile Transition and Excess Volatility in Supply Chain Networks

We study a production network in which firms use non-substitutable (Leontief) inputs, hold precautionary inventories and face idiosyncratic productivity shocks, with adjustment occurring through quantities rather than prices. We show analytically and numerically that a critical boundary exists in the space of shock volatility and inventory holdings: above this threshold, the economy absorbs shocks and fluctuates mildly while below it, cascading shortages make system-wide crises inevitable. Close to the threshold, aggregate output volatility diverges through network-mediated amplification of purely idiosyncratic shocks, providing a concrete mechanism for the ``small shocks, large business cycles'' puzzle. Because inventories are costly, competitive pressure drives firms toward the fragility boundary: a resilience-efficiency trade-off emerges, putting the gains from lean supply chains at risk. Finally, we show that supplier diversification shifts the threshold and, depending on its abundance, can eliminate the fragile regime entirely.

physics.soc-ph↗

arXiv2025

A differentiable model of supply-chain shocks

Modelling how shocks propagate in supply chains is an increasingly important challenge in economics. Its relevance has been highlighted in recent years by events such as Covid-19 and the Russian invasion of Ukraine. Agent-based models (ABMs) are a promising approach for this problem. However, calibrating them is hard. We show empirically that it is possible to achieve speed ups of over 3 orders of magnitude when calibrating ABMs of supply networks by running them on GPUs and using automatic differentiation, compared to non-differentiable baselines. This opens the door to scaling ABMs to model the whole global supply network.

physics.soc-ph↗

arXiv2025

Critical fragility in socio-technical systems

Socio-technical systems, where technological and human elements interact in a goal-oriented manner, provide important functional support to our societies. Here we draw attention to the underappreciated concept of timeliness -- i.e., system elements being available at the right place at the right time -- that has been ubiquitously and integrally adopted as a quality standard in the \textit{modus operandi\/} of socio-technical systems. We point out that a variety of incentives, often reinforced by competitive pressures, prompt system operators to myopically optimize for efficiencies, running the risk of inadvertently taking timeliness to the limit of its operational performance, correspondingly making the system critically fragile to perturbations by pushing the entire system towards the proverbial `edge of a cliff'. Invoking a stylized model for operational delays, we identify the limiting operational performance of timeliness, as a true critical point, where the smallest of perturbations can lead to a systemic collapse. Specifically for firm-to-firm production networks, we suggest that the proximity to \textit{critical fragility\/} is an important ingredient for understanding the fundamental ``excess volatility puzzle'' in economics. Further, in generality for optimizing socio-technical systems, we propose that critical fragility is a crucial aspect in managing the trade-off between efficiency and robustness.

physics.soc-ph↗

arXiv2024

Timeliness criticality in complex systems

In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases, (universal) critical exponents, and related dynamical properties. Here we consider the functionality of systems, notably operations in socio-technical ones, production in economic ones and, more generally, any schedule-based system, where timing is of crucial importance. We introduce a stylized model of delay propagation on temporal networks, where the magnitude of delay-mitigating buffer acts as a control parameter. The model exhibits {\it timeliness criticality}, a novel form of critical behavior. We characterize fluctuations near criticality, commonly referred to as ``avalanches'', and identify the corresponding critical exponents. The model exhibits timeliness criticality also when run on real-world temporal systems such as production networks. Additionally, we explore potential connections with the Mode-Coupling Theory of glasses, the depinning transition and the directed polymer problem.

physics.soc-ph↗

arXiv2024

Revisiting Granular Models of Firm Growth

We revisit granular models that represent the size of a firm as the sum of the sizes of multiple constituents or sub-units. Originally developed to address the unexpectedly slow reduction in volatility as firm size increases, these models also explain the shape of the distribution of firm growth rates. We introduce new theoretical insights regarding the relationship between firm size and growth rate statistics within this framework, directly linking the growth statistics of a firm to how diversified it is. The non-intuitive nature of our results arises from the fat-tailed distributions of the size and the number of sub-units, which suggest the categorization of firms into three distinct diversification types: well-diversified firms with sizes evenly distributed across many sub-units, firms with many sub-units but concentrated size in just a few, and poorly diversified firms consisting of only a small number of sub-units. Inspired by our theoretical findings, we identify new empirical patterns in firm growth. Our findings show that growth volatility, when adjusted by average size-conditioned volatility, has a size-independent distribution, but with a tail that is much too thin to be in agreement with the predictions of granular models. Furthermore, the predicted Gaussian distribution of growth rates, even when rescaled for firm-specific volatility, remains fat-tailed across all sizes. Such discrepancies not only challenge the granularity hypothesis but also underscore the need for deeper exploration into the mechanisms driving firm growth.

econ.GN↗

arXiv2024

Compositional Growth Models

We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the growth rate of the entity is the addition of the growth rates of the composing units, with possibly heterogeneous weights. We review such models and show that they can be understood through a unifying theoretical framework, explaining the resulting growth rate distributions using mixtures of Gaussians.

econ.GN↗

arXiv2023

Revealing production networks from firm growth dynamics

We study the correlation structure of firm growth rates. We show that most firms are correlated because of their exposure to a common factor but that firms linked through the supply chain exhibit a stronger correlation on average than firms that are not. Removing this common factor significantly reduces the average correlation between two firms with no relationship in the supply chain while maintaining a significant correlation between two firms that are linked. We then investigate if this observation can be used to reconstruct the topology of a supply chain network using Gaussian Markov Models.

q-fin.ST↗

arXiv2022

Exact time-dependent dynamics of discrete binary choice models

We provide a generic method to find full dynamical solutions to binary decision models with interactions. In these models, agents follow a stochastic evolution where they must choose between two possible choices by taking into account the choices of their peers. We illustrate our method by solving Kirman and Föllmer's ant recruitment model for any number $N$ of agents and for any choice of parameters, recovering past results found in the limit $N\to \infty$. We then solve extensions of the ant recruitment model for increasing asymmetry between the two choices. Finally, we provide an analytical time-dependent solution to the standard voter model and a semi-analytical solution to the vacillating voter model.

cond-mat.stat-mech↗

arXiv2021

Out-of-Equilibrium Dynamics and Excess Volatility in Firm Networks

We study the conditions under which input-output networks can dynamically attain a competitive equilibrium, where markets clear and profits are zero. We endow a classical firm network model with minimal dynamical rules that reduce supply/demand imbalances and excess profits. We show that the time needed to reach equilibrium diverges to infinity as the system approaches an instability point beyond which the Hawkins-Simons condition is violated and competitive equilibrium is no longer admissible. We argue that such slow dynamics is a source of excess volatility, through accumulation and amplification of exogenous shocks. Factoring in essential physical constraints absent in our minimal model, such as causality or inventory management, we then propose a dynamically consistent model that displays a rich variety of phenomena. Competitive equilibrium can only be reached after some time and within some restricted region of parameter space, outside of which one observes spontaneous periodic and chaotic dynamics, reminiscent of real business cycles. This suggests an alternative explanation of excess volatility in terms of purely endogenous fluctuations. Diminishing return to scale and increased perishability of goods are found to ease convergence towards equilibrium.

econ.GN↗

arXiv2021

From Ants to Fishing Vessels: A Simple Model for Herding and Exploitation of Finite Resources

We analyse the dynamics of fishing vessels with different home ports in an area where these vessels, in choosing where to fish, are influenced by their own experience in the past and by their current observation of the locations of other vessels in the fleet. Empirical data from the boats near Ancona and Pescara shows stylized statistical properties that are reminiscent of Kirman and Föllmer's ant recruitment model, although with two ant colonies represented by the two ports. From the point of view of a fisherman, the two fishing areas are not equally attractive, and he tends to prefer the one closer to where he is based. This piece of evidence led us to extend the original ants model to a situation with two asymmetric zones and finite resources. We show that, in the mean-field regime, our model exhibits the same properties as the empirical data. We obtain a phase diagram that separates high and low herding regimes, but also fish population extinction. Our analysis has interesting policy implications for the ecology of fishing areas. It also suggests that herding behaviour here, just as in financial markets, will lead to significant fluctuations in the amount of fish landed, as the boat concentration on one area at a given point in time will diminish the overall catch, such loss not being compensated by the reproduction of fish in the other area. In other terms, individually rational behaviour will not lead to collectively optimal results.

physics.soc-ph↗

arXiv2020

Schrödinger's ants: A continuous description of Kirman's recruitment model

We show how the approach to equilibrium in Kirman's ants model can be fully characterized in terms of the spectrum of a Schrödinger equation with a Pöschl-Teller ($\tan^2$) potential. Among other interesting properties, we have found that in the bimodal phase where ants visit mostly one food site at a time, the switch time between the two sources only depends on the ``spontaneous conversion" rate and not on the recruitment rate. More complicated correlation functions can be computed exactly, and involve higher and higher eigenvalues and eigenfunctions of the Schrödinger operator, which can be expressed in terms of hypergeometric functions.

physics.soc-ph↗

arXiv2020

By Force of Habit: Self-Trapping in a Dynamical Utility Landscape

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory effects and habit formation may dominate over utility maximisation. We propose a stylized model with a history-dependent utility function where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing effects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find in particular that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behaviour.

cond-mat.stat-mech↗

arXiv2019

May's Instability in Large Economies

Will a large economy be stable? Building on Robert May's original argument for large ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the economy towards marginal stability. We study networks of firms in which inputs for production are not easily substitutable, as in several real-world supply chains. Relying on results from Random Matrix Theory, we argue that such networks generically become dysfunctional when their size increases, when the heterogeneity between firms becomes too strong or when substitutability of their production inputs is reduced. At marginal stability and for large heterogeneities, we find that the distribution of firm sizes develops a power-law tail, as observed empirically. Crises can be triggered by small idiosyncratic shocks, which lead to "avalanches" of defaults characterized by a power-law distribution of total output losses. This scenario would naturally explain the well-known "small shocks, large business cycles" puzzle, as anticipated long ago by Bak, Chen, Scheinkman and Woodford.

physics.soc-ph↗

arXiv2018

Greedy algorithms and Zipf laws

We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in the cases $K=1$ and $K \to \infty$. The resulting stationary distribution of sizes is generically a Zipf-law provided $M > K/2$. When $M \leq K/2$, no selection occurs and the size distribution remains thin-tailed. In the special case $M=K$, one needs to regularise the problem by introducing a small "default" probability $ϕ$. We find that the stationary distribution has a power-law tail that becomes a Zipf-law when $ϕ\to 0$. The approach to the stationary state can also been characterized, with strong similarities with a simple "aging" model considered by Barrat & Mézard.

cond-mat.stat-mech↗