Yougui Wang

The circulation of money and holding time distribution

We have studied the statistical mechanics of money circulation in a closed economic system. An explicit statistical formulation of the circulation velocity of money is presented for the first time by introducing the concept of holding time of money. The result indicates that the velocity is governed by behavior patterns of economic agents. Computer simulations have been carried out in order to demonstrate the shape of the holding time distribution. We find that, money circulation is a Poisson process in which the holding time probability distribution follows a type of Gamma distribution, and the velocity of money depends on the share for exchange and the number of agents.

How required reserve ratio affects distribution and velocity of money

In this paper the dependence of wealth distribution and the velocity of money on the required reserve ratio is examined based on a random transfer model of money and computer simulations. A fractional reserve banking system is introduced to the model where money creation can be achieved by bank loans and the monetary aggregate is determined by the monetary base and the required reserve ratio. It is shown that monetary wealth follows asymmetric Laplace distribution and latency time of money follows exponential distribution. The expression of monetary wealth distribution and that of the velocity of money in terms of the required reserve ratio are presented in a good agreement with simulation results.

Effects of saving and spending patterns on holding time distribution

Abstract.The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly, and a power law when the saving factor is set diversely. The power distribution can also be obtained by proposing a new model where the preferential spending behavior is considered. The association of the distribution with the probability of money to be exchanged has also been discussed.

The Economic Mobility in Money Transfer Models

In this paper, we investigate the economic mobility in four money transfer models which have been applied into the research on wealth distribution. We demonstrate the mobility by recording the time series of agents’ ranks and observing their volatility. We also compare the mobility quantitatively by employing an index, “the per capita aggregate change in log-income”, proposed by economists. Like the shape of distribution, the character of mobility is also decided by the trading rule in these transfer models. It is worth noting that even though two models have the same type of distribution, their mobility characters may be quite different.

The velocity of money in a life-cycle model

The determinants of the velocity of money have been examined based on life-cycle hypothesis. The velocity of money can be expressed by reciprocal of the average value of holding time that is defined as interval between participating exchanges for one unit of money. This expression indicates that the velocity is governed by behavior patterns of economic agents and opens a way for constructing micro-foundation of it. It is found that time pattern of income and expense for a representative individual can be obtained from a simple version of life-cycle model, and average holding time of money resulted from the individuals optimal choice depends on the expected length of relevant planning periods.

Technological innovation, business cycles and self-organized criticality in market economies

In the market economies, sustained output growth is always accompanied by persistent fluctuations. Whether the fluctuations are caused by external shocks or deterministic forces has been a controversial issue in economics, with the dominant mainstream paradigm favouring the former. Here we examine the hypothesis that an important determinant of periods and sizes of expansion and recession is the constructive and destructive effects of innovations and the consequent chain reactions. We show that an evolutionary two-dimensional Bak-Sneppen model is able to generate results which are very similar to the empirical fluctuations which we observe in GDP dynamics of OECD countries. The finding provides a different framework for understanding aggregate market dynamics from that of conventional economic theory.

Prospects for Money Transfer Models

Recently, in order to explore the mechanism behind wealth or income distribution, several models have been proposed by applying principles of statistical mechanics. These models share some characteristics, such as consisting of a group of individual agents, a pile of money and a specific trading rule. Whatever the trading rule is, the most noteworthy fact is that money is always transferred from one agent to another in the transferring process. So we call them money transfer models. Besides explaining income and wealth distributions, money transfer models can also be applied to other disciplines. In this paper we summarize these areas as statistical distribution, economic mobility, transfer rate and money creation. First, money distribution (or income distribution) can be exhibited by recording the money stock (flow). Second, the economic mobility can be shown by tracing the change in wealth or income over time for each agent. Third, the transfer rate of money and its determinants can be analyzed by tracing the transferring process of each one unit of money. Finally, money creation process can also be investigated by permitting agents go into debts. Some future extensions to these models are anticipated to be structural improvement and generalized mathematical analysis.

Dependence of Distribution and Velocity of Money on Required Reserve Ratio

The impacts of money creation on the statistical mechanics of money circulation were investigated by focusing on the dependence of monetary wealth distribution and the velocity of money on the required reserve ratio in this paper. In reality, money creation is important to economic system. The process of money creation can be represented by the multiplier model of money in traditional economics. From this model, it can be known that the required reserve ratio set by the central bank is one of the main determinants of the monetary aggregate and under some assumptions the monetary aggregate can be expressed as the product of the monetary base and the required reserve ratio in steady state. Taking the role that the required reserve ratio plays in the monetary system into account, we developed a random transfer model by introducing a fractional reserve banking system and carried out some simulations to observe how the monetary aggregate evolves over time, how monetary wealth is distributed among agents, as well as how fast money is transferred in the transferring process. Monetary wealth is found to follow asymmetric Laplace distribution, and the fact that latency time of money follows exponential distribution indicates that the transferring process is Poisson type. The theoretical formulas of monetary wealth distribution and the velocity of money in terms of the required reserve ratio are given respectively which are in a good agreement with the simulation results.

Emergence of Fair Offers in Ultimatum Game

The dynamics of how fair offers come about in ultimatum game is studied via the method of agent-based modeling. Both fairness motive and adaptive learning are considered to be important in the fair behavior of human players in concerning literature. Here special attention is paid to situations where adaptive learning proposers encounter responders with either pure money concern or fairness motivation. The simulation results show that the interplay of adaptive learning participants yields a perfect sub-game equilibrium, but fair offers will be provided by proposers as long as a small proportion of responders play “tough” against unfair offer.