William J. baumol and Edward Wolff studied the problem of chaotic economy from the perspective of microeconomics. 1983, they are considering the research and development of enterprises (r&; D) The relationship between expenditure level and enterprise production growth can be found in R & When the proportion of D expenditure level to enterprise sales income reaches a certain range, the enterprise production growth rate will appear cyclical or chaotic.
1985, baumol and R.E.Quandt published a paper "Chaos Model and Predictability", and studied the relationship model between profit and advertising: Pt=aYt( 1-yt), where Pt is the total profit and YT is the advertising expenditure at t, and they assumed that the manufacturer would press. That is, Yt+ 1=b×Pt, then under the condition of a×b=α, yt+1= α× yt (1-yt) can be obtained; The research shows that after a period of time, this relationship model will appear large oscillation and even chaos. Dai (R. Day, 1982, 1983) studied the classical economic growth model including net natural birth rate, production function and average wage income. If the income of the largest population is lower than the income needed to maintain the minimum living standard, the population changes will be chaotic. He and Benhbib (198 1) have also studied that different consumption tendencies will produce different consumption behaviors: the consumption choices of the poor are likely to be quite stable, while the consumption behaviors of the rich may be periodic or even chaotic. The research of Boldrin (1988) shows that the irregular fluctuation of economic phenomena is the result of endogenous decision of economic system under the joint action of market forces, technological changes and consumption tendency. J. b. rosser( 1993) and others made an empirical explanation with the economic reform of Eastern European countries. The socialist economy planned by the central government will not only appear periodic fluctuations, but also chaos, and the condition for entering chaos is often when the economic system changes will happen. In 1992, D.P.Decoster and D.W.Mitchell studied the chaos of monetary dynamic system. Blauch (1988), Schenkman (1986) and others put forward the methods of correlation, "mixing" and "residual" to diagnose the chaos of economic time series. Sayers, Barnett, Frank and others also found low-dimensional chaotic attractors in the economic activities that produce high-frequency economic data in stock securities, foreign exchange transactions, futures and other markets. This means that only a few economic variables can describe such a complex economic phenomenon.
In China, from 65438 to 0987, American economist Chen Ping calculated the fractal dimension with actual data, and found a strange attractor with a dimension of about 1.5 from the macro monetary index. Since the study of chaos economics was introduced into China, Yang Peicai and others have studied the strange attractor in the foreign exchange system in the paper "Examples and Predictability of Economic Chaos" published by 1992, taking the weekly average exchange rate time series of the British pound against the US dollar as the original data, and deduced the regularity and recent predictability of exchange rate changes. 1993. Wang Jun et al. in Standard & Poor's 500 Index; P 500) points out that s&; 500 has a chaotic attractor with a dimension of 2.33, and the significance of this attractor to the capital market movement is discussed. Liu Hong used the theory and method of system engineering to demonstrate the conditions for Douglas production function to produce chaos. From 65438 to 0994, Huang and Li studied the fractal characteristics in the economic system in their book Theory and Method of Nonlinear Economics. For the first time, they used some statistical methods and forecasting methods of nonlinear economics (BDS statistics and R/S analysis) to forecast and empirically study the price of gold in Hong Kong and the price of Shenzhen stock market. At present, more and more domestic scholars are engaged in the study of chaotic economy. For example, Zhuang Xintian and others use chaotic economics to analyze the liquidity of the stock market and the changes in the number of trading groups, and discuss how to realize the liquidity and equilibrium of the market. Wang Chunfeng and Conquer used chaos economics and VAR method to make an empirical analysis on the causes and development trend of deflation in China. According to the data of our national economy, Shen and others put forward a theoretical model to prove economic chaos.
In the future, we should strengthen the research on economic chaos from two aspects: expanding the empirical scope of economic chaos and improving the quality of empirical research; In order to make a breakthrough in control and prediction, it is necessary to study the dynamic model of economic system in depth. The contribution of the development of chaotic economics to economics will be immeasurable, which will lead to the reform of mathematical economics and econometrics, thus it is possible to establish a unified economic theory that includes all schools in the past under the new norms and better explain the operating laws of modern economy.