Discussion Paper

No. 2008-36 | December 10, 2008
Modeling Maximum Entropy and Mean-Field Interaction in Macroeconomics


The representation of the economic system, from a complexity perspective, focuses on interactions among heterogeneous agents in conditions of uncertainty. Heterogeneity entails asymmetric reactions to shocks and, through interaction mechanisms and feedback loops at micro, macro and meso level, these diverse reactions influence behaviours of other agents. Such a system cannot be modelled with mainstream economics’ tools. In this work we propose a stochastic dynamic model with heterogeneous firms. Their responses to stochastic shocks, in order to maximize profit, modifies their financial ratios, determining in this way the evolution of the system. The model is analytically solved by means of maximum entropy maximization and master equation’s solution techniques (Aoki and Yoshikawa, 2006).

Paper submitted to the special issue "Reconstructing Macroeconomics

JEL Classification

E1 E6

Cite As

Corrado Di Guilmi, Mauro Gallegati, and Simone Landini (2008). Modeling Maximum Entropy and Mean-Field Interaction in Macroeconomics. Economics Discussion Papers, No 2008-36, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2008-36


Comments and Questions

Enrico Scalas - Some suggestions for the authors
February 03, 2009 - 10:23

In this paper, the authors introduce a continuous-time Markov model for the time evolution of a system of heterogeneous and interacting agents partitioned into groups or states. Firm behaviour is modelled following [1] and [2].

I have the following (minor) suggestions:

1. English language

There are several ...[more]

... mistakes both in English spelling and grammar. One of the authors (Di Guilmi) has an affiliation in an English-speaking country. It should be easy to find an English-speaking colleague helping in reading and revising the paper.

2. Style of the paper

Some readers with a more mathematical background might find difficult reading this paper as it is not written in the usual style (definition, lemma, theorem, etc.). For this part of the readership, it would be useful to state the main results as theorems or propositions with hypotheses made
explicit. This could be done by extending the appendix.

3. Conclusion section

The concluding remarks contain only a summary of the paper and there is no discussion of the scope and meaning of the results as well as of the limits of the mean-field approximation for interactions.


[1] Greenwald, B. and Stiglitz, J. E. (1993): Financial markets imperfections and business cycles, Quarterly journal of Economics, 108(1).

[2] Delli Gatti, D., Di Guilmi, C., Gaffeo, E., Giulioni, G., Gallegati,
M. and Palestrini, A. (2005): A new approach to business fluctuations:
heterogeneous interacting agents, scaling laws and financial fragility, Journal of Economic Behavior and Organization, 56(4).

Corrado Di Guilmi, Mauro Gallegati, Simone Landini - Enrico Scalas' comment
April 28, 2009 - 04:53

We thank Enrico Scalas for his precious suggestions. We are revising the paper according to points 1 and 3. As regards point 2, even though we agree that structuring the paper in terms of theorem, lemmas, etc... would be pleasant for mathematicians, we believe a structure like the one ...[more]

... adopted is more suitable for economists who are generally not supposed to be familiar with the employed mathematical and theoretical physics tools. In our opinion, thanks to this approach - which concentrates more on developing and spreading topics’ meaning and usefulness, rather than formalizing them - the reader is softly driven even through the hardest mathematical steps.