We use a simple chartist–fundamentalist model developed by Day and Huang to explore recent chaos control algorithms as potential candidates for central bank intervention rules. We find that methods such as delayed feedback control, OGY and constant feedback have, in principle, the potential to reduce exchange rate variability and deviations from fundamentals even in the presence of large dynamic noise.
The chartist–fundamentalist approach (e.g., Day and Huang, 1990, Huang and Day, 1993, Brock and Hommes, 1998, Lux and Marchesi, 2000, Chiarella et al., 2002, Farmer and Joshi, 2002 and Rosser et al., 2003) has proven to be quite successful in replicating the stylized facts of financial markets. For instance, some of the more recent contributions generate artificial data that is hard to discriminate from actual data. Although buffeted with dynamic noise, price dynamics are at least partially due to an endogenous nonlinear law of motion. Such nonlinearity may originate from the fact that traders use nonlinear trading rules to determine their investment position.
If price fluctuations are stimulated endogenously, central authorities may have some chance to control the dynamics. Indeed, recently some methods to stabilize chaotic behavior have been introduced (Schuster, 1999). First, the OGY method, named after Ott et al. (1990), or the delayed feedback control (DFC) method of Pyragas (1992) may be used to stabilize unstable periodic orbits embedded within a chaotic attractor. While the OGY method slightly perturbs an accessible system parameter, the DFC method adds a linear feedback to the system. Second, the constant feedback (CF) method (e.g., Parthasarathy and Sinha, 1995 and Wieland, 2002) is used to suppress chaos.
The aim of this paper is to investigate chaos control methods within the chartist–fundamentalist approach. Specifically, we study whether the chaos control literature offers ways to improve the effectiveness of central bank interventions. Our analysis is based on the seminal work of Day and Huang, which we adjust to foreign exchange markets. The contribution of Day and Huang not only established the study of models with chartists and fundamentalists on a sophisticated scientific level but also produced many descendants (Lux and Marchesi, 2002).
Although the empirical literature is ambivalent about the usefulness of intervention operations, central banks intervene quite frequently in foreign exchange markets (e.g., LeBaron, 1999, Neely, 2001 and Sarno and Taylor, 2001). As it turns out, the two most common heuristic intervention strategies “leaning against the wind” and “targeting long-run fundamentals” are somehow related to concepts discussed in the chaos control literature. Our paper provides an analytical and numerical underpinning of central bank intervention strategies. Given the policy importance of central bank interventions, it is surprising that this aspect has until now received only scant attention in the literature.
Our main results are as follows. While “leaning against the wind” fails to stabilize the market, “targeting long-run fundamentals” may reduce both volatility and distortion. In order for the latter method to work, however, central banks have to intervene quite considerably. If they fail to do so, the exchange rate may not be driven towards fundamentals. The OGY method in our model is a more sophisticated version of “targeting long-run fundamentals.” For instance, this rule is only activated if the exchange rate lies within a promising intervention zone. With the CF method, central banks have the opportunity to direct the exchange rate towards a desired level while simultaneously reducing volatility.
The paper is organized as follows. In Section 2, we briefly present the model of Day and Huang. In Section 3, we extend the model by noise traders and a central bank. In addition, we explore the workings of DFC (Section 3.2), OGY (Section 3.3) and CF (Section 3.4). In Section 4, we discuss the methods. The final section concludes the paper.
According to the chartist–fundamentalist approach, exchange rate fluctuations are at least partially due to an endogenous nonlinear law of motion. Clearly, if the dynamics is not fully exogenous, central authorities may have the opportunity to stabilize the markets. The aim of this paper is to explore and design central bank intervention strategies, taking into account recent findings from the chaos control literature.
Using the model of Day and Huang as a foreign exchange market laboratory, we compare the working of three recently developed chaos control mechanisms. Delayed feedback control in the form of “targeting long-run fundamentals” proved to be effective if applied courageously enough. “Leaning against the wind” has no potential to stabilize the market. The OGY method allows the central bank to reduce both distortion and volatility. With the constant feedback method, the central bank has an instrument to shift the exchange rate away from fundamentals. At least in the short run, central banks may thus conduct a “beggar your neighbor policy.”
Empirical studies do not agree whether central bank interventions may stabilize the market or not. We would like to stress that chaos control methods deliver a strong theoretical background for the working of these methods. We therefore hope that our paper may stimulate further research (e.g. within a standard foreign exchange rate model, such as the model of Dornbusch, 1976), enriched by chartists and fundamentalists so that the effectiveness of central bank interventions can be better understood.
