درباره ویژگی های بازارهای سهام مصنوعی: فرضیه بازار کارآمد و فرضیه انتظارات عقلایی

By studying two well known hypotheses in economics, this paper illustrates how emergent properties can be shown in an agent-based artificial stock market. The two hypotheses considered are the efficient market hypothesis and the rational expectations hypothesis. We inquire whether the macrobehavior depicted by these two hypotheses is consistent with our understanding of the microbehavior. In this agent-based model, genetic programming is applied to evolving a population of traders learning over time. We first apply a series of econometric tests to show that the EMH and the REH can be satisfied with some portions of the artificial time series. Then, by analyzing traders’ behavior, we show that these aggregate results cannot be interpreted as a simple scaling-up of individual behavior. A conjecture based on sunspot-like signals is proposed to explain why macrobehavior can be very different from microbehavior. We assert that the huge search space attributable to genetic programming can induce sunspot-like signals, and we use simulated evolved complexity of forecasting rules and Granger causality tests to examine this assertion.

While it is claimed quite frequently that the stock market is a complex adaptive system, conventional financial models, constrained by computing power, are not capable of demonstrating this feature. However, recent progress in computing technology has made possible a more ambitious vehicle to construct and simulate the stock market. The fledgling research field, known as the artificial stock market, is distinguished from the conventional model-building in many essential ways.1 Generally speaking, models in this field are composed of many heterogeneous interacting adaptive traders. The conventional devices such as the rational expectations hypothesis and the representative agent are discarded (Arthur, 1992). In principle, the artificial stock market is a promising way to study the stock market as a complex adaptive system. By that, we mean two things. First, the artificial stock market is rich in dynamics. Second, it is rich in emergent properties.2 The rich dynamics of the artificial stock market have been documented in the literature. One of the early attempts of this research was to show that many econometric properties (stylized facts) of financial time series can be replicated by artificial stock markets. The properties replicated include volatility clustering (autoregressive conditional heteroskedasticity (ARCH)), excess kurtosis (fat-tail distribution), bubbles and crashes, chaos, unit roots, and many others.3Thus, there is little doubt that the artificial stock market can generate rich dynamics. However, being able to generate rich dynamics is only a minor part of complex adaptive systems. To be a complex adaptive system, rich dynamics must be generated endogenously (or from bottom up), rather than be given exogenously (top down). It is this difference that leads to the main characteristic of complex adaptive systems, namely, emergence. Emergence is about “how large interacting ensembles exhibit collective behavior that is very different from anything one may have expected from simply scaling up the behavior of the individual units” (Krugman, 1996, p. 3), or “…in a structured system, new properties emerge at higher levels of integration which could not have been predicted from a knowledge of the lower level components” (Mayr, 1997, p. 19). Examples of emergence abound in other fields (Holland, 1998), and economists are anything but unfamiliar with the significance of this term. Apart from the Santa Fe Institute Economists, Krugman (1996) and Epstein and Axtell (1996) are among the first few economists who exemplified emergence with a series of economic phenomena. Nevertheless, the emergent properties of the artificial stock market has not received a full attention. This paper considers a different research direction. Instead of replicating the econometric properties of financial time series, though it is still worth doing, we are concerned with identifying some areas of the artificial stock market where the phenomena observed can be plausibly argued as emergent behavior. The areas considered in this paper are two celebrated hypotheses in economics and finance, namely, the efficient market hypothesis (EMH) and the rational expectations hypothesis (REH). First, the efficient market hypothesis. What does it mean if the EMH can be an emergent property? Consider the EMH as a collective behavior. It would be an emergent property if it is not expected from our understanding of the behavior of individual traders. Let us take an extreme case. Suppose that none of the traders believe in the EMH, then this property will not be expected to be a feature of their collective behavior. Even if it is observed, it has no direct link to the individual behavior. So, if the collective behavior of these traders indeed satisfies the EMH as tested by the standard econometric procedures, then we would consider the EMH as an emergent property. Second, the rational expectations hypothesis. Consider the rational expectations hypothesis as a collective behavior. It would be an emergent property if all our traders are boundedly rational, with their collective behavior satisfying the REH as tested by econometrics. This way of identifying the EMH and the REH as emergent properties may not seem rigorous, since the word “expected” or “surprising” is somewhat subjective. Nonetheless, in the light of the long-lasting debate on the two hypotheses, this particular way of defining emergent properties is quite normal, if not satisfactory. In a sense, it provides a new perspective to reflect upon these controversies. Consider a spectrum. On the leftmost are individuals, and the rightmost an aggregate of individuals (the representative agent). It seems much easier to reject these hypotheses at the leftmost point than at the other extreme. To the leftmost is the area of psychology, where evidence of bounded rationality dates back to 1970s (Tversky and Kahneman, 1974), whereas to the rightmost is the turf of the representative agent whose rational behavior has been evidenced by advanced econometrics since Hall’s work (1978) on consumption theory in 1978. Therefore, instead of thinking of this spectrum as an encapsulation of conflicting viewpoints, one may consider it a system whose microbehavior is rather different from macrobehavior (Kirman, 1992). Of course, this manner of thinking is nothing new in economics. A list of early examples, such as Adam Smith’s invisible hand and Hayek’s hypothesis, was well documented in Krugman (1996). However, what has not been done in conventional economics is to construct a system (artificial society) where to allow both views of the world are represented. What we have in mainstream economics is a highly abstract representative agent. Under these circumstances, there is no distinction between the microbehavior and the macrobehavior of traders, and hence, no room for the study of emergent properties. Recent advancement in research technology provides us with an opportunity to address the issue. This paper is not the first one in this line of research, and certainly not the last. What distinguishes this study from earlier ones, however, is that this study may be viewed as a first attempt to formally interpret the EMH and the REH as emergent properties in the context of artificial stock markets. The rest of the paper is organized as follows. In Section 2, we present the analytical model upon which our artificial stock market is built. Genetic programming is introduced in Section 3 to model a population of traders learning over time. We then present and analyze the results of simulations in 4 and 5. A series of econometric tests and microstructure analysis were conducted to show that the EMH and REH can be emergent properties which will be further discussed in Section 6. Concluding remarks are given in Section 7.

By following some standard or modern econometric procedures, this paper examines the aggregate behavior of time series generated by an agent-based artificial stock market. The tests show that some series examined cannot reject a version of the efficient market hypothesis or a version of the rational expectations hypothesis. Thus, we illustrate, to a certain extent, how agent-based models are capable of replicating some well known economic behavior empirically. However, the properties shown as aggregate results can be quite different from what we observe from the individual behavior. In this paper, the aggregate result of the efficient market can be generated from a collection of interacting traders, most of whom do not believe in the martingale hypothesis (the efficient market hypothesis). Moreover, the aggregate result of the rational expectations can be generated from a collection of boundedly rational agents who behave as if they were never sure about the true model and were continuously searching for a better forecasting model. As a result, the aggregate results are not anticipated from simple scaling-up of the individuals, which is what one may call emergent properties in the literature. We would like to make a few final remarks about the work done in this study. Firstly, this paper can be read as an extension of the research line stressing that macroeconomic behavior is not a simple scaling-up of microeconomic behavior, e.g. Kirman (1992). More specifically, it is closely related to the agent-based computational model, populated by Epstein and Axtell (1996). This type of model allows us to trace a bottom-up path which is infeasible for conventional models built upon the device of the representative agent, and hence provides an ideal tool to show more precisely how microeconomic behavior can be quite different from macroeconomic behavior. Demonstrating the possibility of this kind of inconsistency is important because it places restrictions on inferring individual behavior from aggregate results. Such restrictions can be critical to policy issues such as decisions to launch a national annuity program based upon a test for the permanent income hypothesis. Secondly, in terms of agent-based modeling of artificial stock markets, this paper can also be related to the Santa Fe Artificial Stock Market (Arthur et al., 1997). While at this moment this field is too young to define a unified or standard framework, there are still interesting comparisons to be made. First, like the SFI approach, this paper can generate rich varieties of market dynamics. We believe that these types of models offer a promising direction to enrich current studies on microstructure and anomalies. Second, both papers show that the key to understanding the rich dynamics of markets is the mechanism which allows a population of traders to learn or adapt over time. There are lots of parameters which can result in effectively different mechanisms, and it is still in an early stage to evaluate their potential impact. But, there are also differences between the SFI approach and our approach. The main difference lies in the specific evolutionary computation (EC) technique employed. For them, it is genetic algorithms; for us, it is genetic programming. As Chen and Yeh (1996)asserted, genetic programming can be viewed as a more general way to do the job which used to be done by GAs. However, GP also has its problem when applied to modeling agents’ learning. As we have shown in this paper, GP provides us with a large search space and has a great potential to generate sunspot-like signals which can compete with simple beliefs in any finite number of data points through mutually reinforcing dynamics. While we consider this specific design relevant to the emergent properties studied in this paper, to what extent are they empirically relevant is an issue to be pursued in the future.