بازار کالا، محدود کننده های قیمت و پویایی قیمت سوداگرانه

We develop a behavioral commodity market model with consumers, producers and heterogeneous speculators to characterize the nature of commodity price fluctuations and to explore the effectiveness of price stabilization schemes. Within our model, we analyze how nonlinear interactions between market participants can create either bull or bear markets, or irregular price fluctuations between bull and bear markets through a (global) homoclinic bifurcation. Both the imposition of a bottoming price level (to support producers) or a topping price level (to protect consumers) can eliminate such homoclinic bifurcations and hence reduce market price volatility. However, simple policy rules, such as price limiters, may have unexpected consequences in a complex environment: a minimum price level decreases the average price while a maximum price limit increases the average price. In addition, price limiters influence the price dynamics in an intricate way and may cause volatility clustering.

Commodity prices are, by any standard, extremely volatile. After inspecting 13 primary commodities over the period 1900–1987 (deflated annual data), Deaton and Laroque (1992) found price variation coefficients, defined as the standard deviation over the mean, ranging from 0.17 (bananas) to 0.60 (sugar). In addition, one often observes dramatic boom and bust episodes. For instance, the decline in prices from the highest level reached in the period from 1974 to August 1975 was 67 percent for sugar, 58 percent for sisal, more than 40 percent for cotton and rubber, and more than 25 percent for cocoa and jute (Newbery and Stiglitz, 1981). In a recent study, Osborne (2003) reported that in Ethiopia the price of maize has more than doubled three times over the last 15 years. Not only many developing countries, but also the United States and the European Union, have thus experimented with some form of commodity price stabilization scheme in the past. In particular, attempts have been made to stabilize agricultural commodity markets by means of a commodity buffer stock scheme. The idea of such schemes is to put a certain amount of output into storage in years in which there is a good harvest, thus increasing the price from what it would have been, and to sell output from the storage in years in which there is a small harvest, thus reducing the price from what it would have been. Another prominent example is the oil market. Following the oil crises in the 1970s, many countries built up huge oil reserves in order to influence the market. Demand and supply schedules, storage and fully rational speculators are the key elements in neo-classical commodity market models (Waugh, 1944; Brennan, 1958; Williams and Wright, 1991; Deaton and Laroque, 1992 and Deaton and Laroque, 1996; Chambers and Bailey, 1996; Osborne, 2003). While these models undoubtedly capture some important aspects of commodity markets, their ability to mimic features such as bubbles and crashes is, however, limited. Supporters of these models – in which the markets are efficient by nature – judge commodity price stabilization schemes as unlikely to have a significant beneficial effect (Newbery and Stiglitz, 1981). Contrary to the efficient market hypothesis, however, there is not only widespread populist feeling that speculators are a major cause of price instability, but also theoretical papers have started to explore this aspect. The chartist–fundamentalist approach, developed in the last decade, offers a new and promising alternative behavioral perspective of financial market dynamics. The main feature of this approach is that interactions between heterogeneous agents, so-called chartists and fundamentalists, may generate an endogenous nonlinear law of motion of asset prices. In Day and Huang (1990), Chiarella (1992) and Farmer and Joshi (2002), the nonlinearity originates from nonlinear technical and fundamental trading rules whereas in Kirman (1991), Brock and Hommes (1998) and Lux and Marchesi (2000), the nonlinearity is caused by the agents switching between a given set of predictors. More recent refinements and applications include Chiarella and He (2001), Chiarella et al. (2002) and Westerhoff (2003). Since these models have demonstrated their ability to match the stylized facts of financial markets quite well one may conclude that this framework is suitable to conduct some policy evaluation experiments. This paper aims at developing a commodity market model along the lines of the chartist–fundamentalist approach to characterize price fluctuations and to unravel the potential effects of price limiters. Its main ingredients are as follows: For simplicity, demand and supply schedules are expressed in a reduced log-linear form. Fundamental to the model is the behavior of the speculators who switch between technical and fundamental trading rules to determine their positions in the market. Prices adjust via a log-linear price impact function: Excess supply (demand) decreases (increases) the price. Our model shows that: (i) the chartists are a source of market instability, as commonly believed, (ii) weak reaction of the speculators (either the fundamentalists or the chartists) can push the market to be either a bull or a bear market (through pitchfork bifurcations); and (iii) strong reaction of the speculators causes market prices to switch irregularly between bull and bear markets (through homoclinic bifurcations). Since prices fluctuate in a complex way between bull and bear markets, the model is capable of replicating some features of commodity price motion. The paper then focuses on the impact of simple price limiters as a potential stabilizing mechanism to reduce price fluctuations. Both theoretical analysis and numerical simulations reveal that if a central authority guarantees a minimum price, e.g. to support the producers, volatility declines. Although the price is backed up from below, the average price of the commodity surprisingly decreases, too. Setting up an upper price limit, e.g. to protect consumers from excessive prices, again yields a drop in price variability. However, the average price the consumers have to pay increases. At least at first sight, this result appears to be counterintuitive and should give policy-makers a warning. Simple measures to control prices may have surprising consequences in a nonlinear world. This puzzling outcome is caused by a dynamic lock-in effect. Consider the case of a crash without a price limiter mechanism. Within our model, a bull market turns into a bear market after the price has crossed a critical upper level. A central authority that intervenes successfully against high prices obviously destroys the necessary condition for such a regime shift. As a result, the average price is higher than without an upper price restriction. Moreover, since the price fluctuates at a high level, it reaches the upper price boundary repeatedly so that the buffer stock is likely to run empty rather quickly. We show that one way to counter this problem is to alternate temporarily between an upper and a lower price boundary. The price volatility then decreases, yet the market remains distorted. However, on–off switching of the stabilization mechanism as well as changing the level of price limiters interferes with the price discovery process and may cause severe bubbles and crashes or volatility clustering. As it turns out, price limiters as applied in our model are identical to a recently developed chaos control method. The development of chaos control algorithms was initiated by Ott et al. (1990) (henceforth OGY). Other popular suggestions include, for instance, the delayed feedback control method of Pyragas (1992) or the constant feedback method of Parthasarathy and Sinha (1995). The OGY control scheme and its descendants have been applied in various fields such as mechanics, electronics or chemistry. Economic applications include Kopel (1997), Kaas (1998) or Westerhoff and Wieland (2004). The feasibility of using chaos controllers in reality depends on the complexity and efficiency of the control algorithm. The chaos control process requires measurement of the system's state, generation of a control signal, and the application of the control signal to an accessible system parameter. For instance, the original OGY control scheme requires knowledge of the map and its fixed point. While such information may be identified from observations in natural science applications, chaos control in an economic context is often seen as rather critical. However, Corron et al. (2000) present experimental evidence that chaos control can be accomplished using simple limiters and argue that chaos control can be practically applied to a much wider array of important problems than thought possible until recently. This method, which has been analytically and numerically explored by Wagner and Stoop (2000) and Stoop and Wagner (2003), simply restricts the phase space that can be explored. Suppose that a variable fluctuates between 0<x<10<x<1. A limiter from below resets all values x<hx<h to hh. As a result, the new system may replace previously chaotic behavior with periodic behavior. One advantage of the limiter method is that it does not add complexity to the system by increasing the size of the system's state space. Another advantage is that stabilization may already be achieved by infrequent interventions. As far as we are aware, this paper contains the first economic study of limiters. And indeed, the method is able to decrease price fluctuations quite easily, yet with the (economic) disadvantage of a lock-in effect as stressed above. The remainder of this paper is organized as follows. Section 2 presents a simple commodity market model with heterogeneous interacting agents and, by using stability and bifurcation analysis, Section 3 examines the price dynamics of the model without price limiter mechanisms. In Section 4, we discuss the consequences of single-price limiters for the price dynamics, and in Section 5, we introduce conditional price limiters. The final section concludes the paper.

This paper is concerned with commodity price dynamics. Actual commodity prices fluctuate strongly: Not only is the price volatility high,but also severe bubbles and crashes regularly emerge. Hence,this topic is of great practical importance, particularly for the formulation of economic policy. Although producers and consumers are two primary participants in commodity markets,there are also other participants,such as speculators,who may have a marked effect both on the degree of price variability and on the success of any commodity price stabilization scheme. Within our model,inter actions between heterogeneous agents create complex bull and bear market fluctuations,which resemble the cyclical price dynamics of many commodity markets. Our model shows that: (i) the chartists are a source of market instability,as commonly believed; (ii) weak reaction of the speculators (either the fundamentalists or the chartists) can push the market to be either a bull or a bear market (through pitchfork bifurcations); and (iii) strong reaction of the speculators causes market prices to fluctuate irregularly between bull and bear markets (through homoclinic bifurcations). Furthermore,we investigate how price boundaries,which function identically to a recently suggested chaos control method,affe ct the price dynamics. We find that simple price limits (i) reduce the variability of prices quite strongly,(ii) are likely to shift the price in an adverse direction and (iii) may lead to an unsustainable buffer stock. The results are caused by a dynamic lock-in effect. By restricting the evolution of the price,the dynamics may become stuck in either the bull or the bear market. However,jumpi ng between bottoming and topping price limiters allows a central authority to manage the evolution of the buffer stock. Prices are then temporarily stabilized in the bull market or the bear market. But it should not be overlooked that whenever a central authority introduces a price stabilization scheme it changes the price discovery process. For instance,price limiters may trigger marked bubbles and crashes or volatility clustering. The study of heterogeneous interacting agents has yielded a number of quite sophisticated models which have proven to be quite successful in explaining financial market dynamics. Our simple commodity market model is inspired by this approach and we would finally like to point out some interesting extensions. First of all,one may consider some other popular technical trading rules. For example,agents are often reported to extrapolate the most recent price trend. Moreover,as argued in Chiarella (1992) or Farmer and Joshi (2002),techni cal analysis may be nonlinear. Secondly,agents may involve some adaptive learning processes when choosing a particular trading strategy. For example,the behavior of chartists and fundamentalists may not be constant over time with respect to their reaction coefficients,and , although agents are boundedly rational,they may try to learn those coefficients. Alternatively,agents ’ expectations may follow some adaptive learning processes. Thirdly,agents may incorporate other switching mechanisms. As argued in Brock and Hommes (1998),one may assign each forecast rule a fitness function (which may depend on the historical performance of the rules) and then let the agent select a rule according to its fitness. Higher complexity may also be achieved by switching from a two-speculator type analysis to a real multi-agent market model (Lux and Marchesi, 2000). Of course,the behavior of both the producers and consumers may also be modeled in more detail. For instance,the producers may base their production decision on expected future prices and thus select between different kinds of forecast rules,as modeled in Brock and Hommes (1997). Finally,the working of different price limiter schemes may also be tested in a laboratory setting. Promising work on experimental asset pricing markets has been done by Smith (1991) or Sonnemans et al. (2004).