Agent-based economic models and econometrics

An early version of the paper was presented at the Econophysics Colloquium 2008, August 28–30, 2008, at the University of Kiel, and also at the International Workshop on Nonlinear Economic Dynamics and Financial Market Modelling, October 9–10, 2008, at Peking University. Comments from participants such as Thomas Lux, Carr Hommes, Carl Chiarella, Tony He, and Duo Wang are all gratefully acknowledged. This final version has further benefited from the painstaking review of an anonymous referee and the guest editors of this special issue, Robert Marks and Nick Vriend. The NSC grants 95-2415-H-004-002-MY3 and 98-2410-H-004-045-MY3 are also greatly acknowledged.

In fact, this trend is generally shared in other social sciences to which the agent-based approach is applied (Janssen & Ostrom, 2006).

One can further include social networks to make it become three. However, in this paper, the review is mainly restricted to agent-based financial markets, and so far there has not been much work that has taken social networks into account. We shall, therefore, omit this from this paper. We will come back to visit this issue in the concluding section.

The design of financial markets, such as different trading mechanisms, from a more decentralized pure order-book driven mechanism to a less centralized market-maker mechanism may provide an alternative explanation for stylized facts (Bottazzi et al., 2005; Anufriev & Panchenko, 2009). However, this paper simply has the design of agents as its focus.

By saying so, the authors are aware of the existence of other taxonomies (Hommes, 2006; LeBaron, 2006; Samanidou et al., 2007).

A nice survey of this class of models is given in Hommes (2006).

Brenner (2006) and Duffy (2006) provide rich resources on various learning algorithms used in agent-based modeling.

There is no standard specification of these three types of traders. One way to construct the three-type model is simply to add one more type of trader to the existing two-type model, for example, by adding noise traders to fundamentalists and chartists (Kaizoji, 2003), or adding contrarian traders to the fundamentalists and trend-followers model (Sansone & Garofalo, 2007).

Using the data for the S&P 500 index, from January 1980 to December 2000, Amilon (2008) actually estimated a three-type agent-based financial market model, and found that contrarians have a longer memory than momentum traders when they form their forecasts of the future price. Of course, this is just the beginning in terms of seeing how agent-based financial market models can be quantified so as to communicate with behavioral finance.

The extension into the multinomial logit model is straightforward.

Aoki (2002) provides a theoretical support for the two-type or two-cluster models.

A lengthy review of this literature can be found in Chen (2008).

Diks and van der Weide (2005) actually distinguish the two by calling the former computational finance models, and the latter economic dynamic models.

Mainly for space considerations, the detailed account of each stylized fact will not be given here. The interested reader is referred to the associated reference listed in the last column of Table 1.

Volatility clustering is treated as a source of fat tails (Ghose and Kroner, 1995).

Examples include nonlinear dynamic models, models with latent (or unobserved) variables, and models with missing or incomplete data.

A review of the development of simulation-based econometrics is beyond the scope of this chapter. The interested reader is referred to Gourieroux and Monfort (1996). In addition, the Journal of Applied Econometrics has a special issue on this subject; see its volume 8 (1993).

See Midgley et al. (2007), p. 890, figure 1.

Kirman himself used ∈ and 1 − δ.

In Kirman (1991), each agent tries to assess what the majority opinion is. Each agent observes q_1,t but with some noise. The noise follows a normal distribution \[--><$>{\scr N}\,(0,{{\sigma }^2} ) <$><!--\]. The third parameter considered by Gilli and Winker (2003) is σ².

Unfortunately, a unique series \[--><$>{{\hat{q}}_{1,t}} <$><!--\] is not available from this estimation. The estimation only gives us \[--><$>{{\hat{\theta }}_1} <$><!--\] and \[--><$>{{\hat{\theta }}_2} <$><!--\], which allows us to simulate many equally likely series \[--><$>{{ q}_{1,t}} <$><!--\]. Hence, we are not able to answer the question: between 1991 to 2000, when is the market dominated by fundamentalists and when is it dominated by chartists?

Notice that, both in Winker and Gilli (2001) and Gilli and Winker (2003), whether Equation (19) holds was only examined numerically as in (20), rather than statistically. This is because a formal test had not been proposed then.

In Alfarano et al. (2005, 2006, 2007), the two clusters of traders are defined as fundamentalists and noise traders instead of the fundamentalists and chartists in Kirman (1991, 1993).

Actually, Boswijk et al. (2007) studied a modified version of the standard ABS model. Instead of forecasting price, (2) and (3), agents are assumed to forecast the price-to-cash flow ratios, but the counterpart of the reverting coefficient (α_f) and the extrapolating coefficient (α_c) remains. However, with this modification, the reasonable ranges for these two parameters are: 0 < α_f < 1, and α_c > 1.

Amilon (2008), in fact, modified standard ABS models in many ways, including the agents’ perceived risk of investment, risk preference, fitness measure, and, most importantly, the noise structure. The additional number of parameters actually comes from this extension.

Of course, the two models are associated with different noise structures; hence, they are estimated with different methods. The two-type model is estimated by the maximum likelihood method, and the three-type model is estimated by the efficient method of moments.

In fact, the earliest application of the agent-based financial model to forecasting is Izumi and Okatsu (1996). See also Izumi and Ueda (1999). See Section 4.2.4.