Discussion Paper

No. 2018-1 | January 02, 2018
Money circulation and debt circulation: a restatement of quantity theory of money


Both money and debt are products of credit creation of banks. Money is always circulating among traders by facilitating commodity transactions. In contrast, debt is created by borrowing and annihilated by repayment as it is matured. However, when this creation-annihilation process is mediated by banks which are constrained by a credit capacity, there exists continuous transfer of debt among debtors, which can be defined as debt circulation. This paper presents a multi-agent model in which income determination, credit creation, and credit transaction are integrated. A hypothetical economy composed of a banking system and multiple traders is proposed, in which the traders are allowed to borrow money from the bank once their expenditure cannot be financed by their own funds. In order to demonstrate the circulations of money and debt from the micro view, the authors track the transfer processes of them and collect their holding times respectively. When the traders could afford their expenditures, only money circulation can be observed. However, as they are forced to borrow, the money circulation is accelerated and debt circulation emerges. Both distributions of holding times of money and debt are found to take exponential form due to the random nature of exchanges. The velocity of money circulation is determined by the expending behavior of traders, while the velocity of debt circulation is associated with the repayment behavior of debtors. Consequently, the aggregate income can be decomposed into two parts: one comes from money circulation and the other from debt circulation.

JEL Classification:

E51, E27, G21


  • Downloads: 263


Cite As

Xiaoyun Xing, Wanting Xiong, Liujun Chen, Jiawei Chen, Yougui Wang, and H. Eugene Stanley (2018). Money circulation and debt circulation: a restatement of quantity theory of money. Economics Discussion Papers, No 2018-1, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2018-1

Comments and Questions

Anonymous - Referee report 1
January 15, 2018 - 09:01

see attached file

Yougui Wang - Authors' Responses to the Referee's Report
January 21, 2018 - 16:18

See the attachment.

Yougui Wang - The revised version of manuscript
January 21, 2018 - 16:20

As a supplementary material, we also attach the revised version of our manuscript.

Vladimir Pokrovskii - Comment
January 25, 2018 - 13:43

Any complex system can be described differently: as a whole, using the most generalized concepts and notions, or as collection of many constituents that interact to each other, obeying their own laws. In physics we have thermodynamic and statistical description, in economics --- macroeconomics and ...[more]

... agent-based approaches, and now we are turning to the money circulation.

The main aim of any theory of money circulation is to calculate the amount of money that one needs to run the production. From the macroeconomic point of view, the amount of money can be calculated according to the quantity theory of money – Fisher’s law (Eq. 2), if one knows a characteristic of the system – the velocity of money calculation. Any macroscopic description ought to be complete and consistent, and the Fisher’s law satisfies these requirements, so as the velocity of money calculation, as an arbitrary quantity, can be set in any case, but it does not solve the problem. The authors know about the deficiencies of this approach, but think that introduction of debt circulation allows to improve the theory and help to understand better what is the velocity of money circulation.

However, the ‘quantity theory of money’ is not the proper starting point to understand what is the velocity of money circulation. It is possible that the better approach could be to start with the considering the product circulation accompanied by money circulation, as it was formulated Schinckus with collaborators [Physica A: Statistical Mechanics and its Applications vol, 463, 111 - 122 (2016) ; vol. 493, 228 - 238 (2018)]. The ‘velocity of money circulation’ appears to be not a velocity of money circulation, but a quantity demonstrating efficiency of the money system. One can think that the understanding the true sense of ‘velocity of money circulation’ could help the authors in the proper developing of the agent-based approach to the theory of money calculation.

Yougui Wang - The authors' responses to the comments
January 27, 2018 - 20:59

We really appreciate your concerns on our paper. Actually, after reading your papers recently published in Physica A, we recognize that we share a common interest on the topic of money circulation. We should cite this innovative work in the revised version of our manuscript. The elementary model you have ...[more]

... developed is very interesting and meaningful. We agree with you that the production is an originator of value and the money flow is just a counter part of the flow of products. Thus the integration of the real economy and the monetary economy is necessary for the construction of a completely theoretical analysis. In our work, we investigated the money circulation only by following the monetary stocks and flows but leaving the goods aside. We think this is an appropriate way at current stage to clarify the roles of money and banking in the working of the economies. Please notice that the monetary flows generated by money or debt can both contribute to GDP, and they are only used for the exchanges with final goods and service, no matter who spend them. Nevertheless, we believe the integrated model will be adopted in our future analysis.