arXiv subjects

Cornelia Metzig

Publications and source records attributed to Cornelia Metzig.

3 recordsLinked to original sources

arXiv2018

A Maximum Entropy Method for the Prediction of Size Distributions

We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of constant size, which contains exit of balls and urns (or nodes and edges for the network case). Knowing mean size (degree) and turnover rate, the power law exponent and exponential cutoff can be derived. Our results are confirmed by simulations and by computation of exact probabilities. We also apply this entropy method to reproduce existing results like the Maxwell-Boltzmann distribution for the velocity of gas particles, the Barabasi-Albert model and multiplicative noise systems.

physics.soc-ph↗

arXiv2013

A Model for Scaling in Firms' Size and Growth Rate Distribution

We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a `tent-shaped' growth rate distribution, the scaling relation of the growth rate variance with firm size, and the causality between them. This is achieved under the simple hypothesis that firms compete for a scarce quantity (either aggregate demand or workforce) which is allocated probabilistically. The model allows us to relate size and growth rate distributions. We compare the results of our model to simulations with other scaling relationships, and to similar models and relate it to existing theory. Effects arising from binning data are discussed.

q-fin.GN↗

arXiv2012

Heterogeneous Enterprises in a Macroeconomic Agent-Based Model

We present a macroeconomic agent-based model that combines several mechanisms operating at the same timescale, while remaining mathematically tractable. It comprises enterprises and workers who compete in a job market and a commodity goods market. The model is stock-flow consistent; a bank lends money charging interest rates, and keeps track of equities. Important features of the model are heterogeneity of enterprises, existence of bankruptcies and creation of new enterprises, as well as productivity increase. The model's evolution reproduces empirically found regularities for firm size and growth rate distributions. It combines probabilistic elements and deterministic dynamics, with relative weights that may be modified according to the considered problem or the belief of the modeler. We discuss statistical regularities on enterprises, the origin and the amplitude of endogeneous fluctuations of the system's steady state, as well as the role of the interest rate and the credit volume. We also summarize obtained results which are not discussed in detail in this paper.

q-fin.GN↗