Abstract
In this paper, we study a class of markets, among which we can mention agricultural and energy markets, characterized by seasonality, i.e., in which demand and/or supply conditions cyclically alternate with a precise and known periodicity. We propose a new theoretical framework based on a cobweb model with adaptive expectations, accordingly modified to be consistent with market’s seasonality. The model, consisting in a second-order non-autonomous difference equation, is investigated with the aim of understanding how the periodical nature of the market together with the agents’ expectation formation mechanism affects the resulting dynamics. We analytically prove the emergence of dynamical scenarios that are missing in the classic cobweb model for non-seasonal markets, such as quasi-periodic dynamics and an ambiguous role on stability of the expectation weight. Finally, we discuss their economic rationale with the help of numerical simulations. In such a peculiar economic framework, agents’ learning plays a key role to explain the dynamical properties of economic observables.
Highlights
The supply and/or consumption patterns characterizing some classes of goods are affected by the particular time at which they are produced and/or used, with the outcome of recurrent price fluctuations that follows a broadly predictable sequence
With the help of numerical experiments, we aim at providing an explanation of the following new facts: (a) stabilization can be possible if the agents form their expectations suitably taking into account out-of-phase price dynamics; (b) dynamics arising when phases are uncoupled can significantly change when the agents form their expectations learning from both phases; both periodic, chaotic and quasi-periodic dynamics can emerge, even for the same given market configuration; 14 We remark that it is possible to show that the region defined by (10) is bounded for any ν ∈ (1/2, 1), even if it becomes increasingly large as ν → 1/2
The resulting model exhibits a high degree of complexity in price dynamics, which grounds on the intrinsic peculiarity of the exchanged good, whose market curves are time-varying, and on the consequent possibility for the agents to use and mix information coming from different past market phases in order to form their expectations
Summary
The supply and/or consumption patterns characterizing some classes of goods are affected by the particular time at which they are produced and/or used, with the outcome of recurrent price fluctuations that follows a broadly predictable sequence This peculiarity is referred to as seasonality. Crop production has to be planned in advance and its harvest usually takes place in a single, specific season, giving rise to the well-known “harvest lows” and “post-harvest rally” price behavior (see, e.g., Rahn 1968; Welch et al 2011) Another example consists of energy goods, in particular electricity, whose consumption changes depending on the year period, day of the week or even the hour of the day, and whose production can be in part affected by time as well (e.g., solar energy). It’s worth mentioning that such markets are often characterized by peculiar distributions in economic observables.
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