Discussion Paper

No. 2008-38 | December 10, 2008
A Note on Aoki-Yoshikawa Model
(Published in Special Issue Reconstructing Macroeconomics)


In this paper, we explore a dynamical version of the Aoki and Yoshikawa model (AYM) for an economy driven by demand. We show that when an appropriate Markovian dynamics is taken into account, AYM has different equilibrium distributions depending on the form of transition probabilities. In the version of the dynamic AYM presented here, transition probabilities depend on a parameter c tuning the choice of a new sector for workers leaving their sector. The solution of Aoki and Yoshikawa is recovered only in the case c = 0. All the other possible cases give different equilibrium probability distributions, including the Bose-Einstein distribution.

Paper submitted to the special issue “Reconstructing Macroeconomics

JEL Classification:

D50, A12, J21, C50


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Cite As

Enrico Scalas and Ubaldo Garibaldi (2008). A Note on Aoki-Yoshikawa Model. Economics Discussion Papers, No 2008-38, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2008-38

Comments and Questions

Anonymous - Assessment
January 16, 2009 - 10:21

The present entry considers a dynamic version of the multi-sectoral, demand-driven macro model proposed by Aoki and Yoshikawa (AY). While AY derived an equilibrium distribution of factors across sectors from combinatorial principles – analogous to Boltzmann’s solution for the statistical equilibrium of n particles under conservation of energy – the ...[more]

... authors derive alternative equilibrium distributions under certain assumptions on the dynamics of factor movements between sectors. With a parameterized family of transition probabilities, a generalized Polya distribution is obtained. Overall, I found this a nice and concise contribution to the new statistical approach to macroeconomics. As a grain of salt, it should nevertheless be mentioned that the new results in this note all hinge on the relatively strong assumption that all productivities are multiples of the lowest productivity. It seems, however, that this restriction is unnecessary from a certain perspective. If one would allow for deviations from the aggregate equality (5) (i.e. demand equal to supply) because of frictions arising from structural change, a similar outcome might be obtained for the admissible factor movements with arbitrary specification of productivities. The authors might wish to elaborate on this idea.

Mishael Milakovic - Reader Comment
January 27, 2009 - 08:47

see attached file

Victor Yakovenko - Reader Comment
January 29, 2009 - 08:43

This paper presents a nice generalization of the AY model using Markovian dynamics. In this generalization, the transition probability of labor between different sectors of economy depends not only on the occupation numbers of the initial states, but also on the occupation numbers of the final states. As ...[more]

... a result, the stationary probability distribution of labor between different sectors is described a generalized formula, which reduces, in the appropriate limiting cases, to the Boltzmann-Gibbs or Bose-Einstein or Fermi-Dirac statistics, well-known in physics.

I agree with the complaints of other commentators about the uninformative title of the paper. First, the book by AY discusses many things, so the title should specify which AY model is being studied. Second, it is not an informative way to title a paper "A note on ...". Tell the reader right away in the title what is the subject or the result of a paper.

Anonymous - Assessment
January 29, 2009 - 21:05

The main innovation respect the A-Y model is that the mobility of workers among the sectors c is variable. See the attached file.

Anonymous - Reader Comment
February 03, 2009 - 08:34

see attached file

Yuji Aruka - Reader Comment
February 12, 2009 - 08:34

see attached file

Anonymous - Reader Comment
February 16, 2009 - 08:38

see attached file

Enrico Scalas - Collective reply
March 13, 2009 - 17:59

This is a collective reply to the seven comments/assessments we received
so-far on the manuscript: ``A Note on Aoki-Yoshikawa Model''. Based on the
comments and on the present reply, we shall resubmit a revised version of
the manuscript.