Real and Financial Interacting Oscillators : A Behavioral Macro-Model with Animal Spirits

In this paper we propose a model in which the real side of the economy, described via a Keynesian good market approach, interacts with the stock market with heterogeneous speculators, i.e., optimist and pessimist fundamentalists. Employing analytical and numerical tools, we detect the mechanisms and the channels through which instabilities get transmitted between markets. In order to perform such analysis, we introduce the "interaction degree approach", which allows us to study the complete three-dimensional system by decomposing it into two subsystems, i.e., the isolated financial and real markets, easier to analyze, that are then interconnected through a parameter describing the interaction degree between the two markets. Next, we derive the stability conditions both for the isolated markets and for the whole system with interacting markets. Finally, we show how to apply the "interaction degree approach" to our model. To this aim, we first classify the possible scenarios according to the stability/instability of the isolated financial and real markets. For each of those frameworks we consider different possible parameter configurations and we show, both analytically and numerically, which are the effects of increasing the degree of interaction between the two markets. In particular, we find that the instability of the real market seems to have stronger destabilizing effects than the instability of the financial market: in fact, the former gets transmitted and possibly amplified by the connection with the financial market, while the latter gets dampened and possibly eliminated by the connection with the real market. We conclude our analysis by showing which are the effects of an increasing bias. Although it is clearly destabilizing when markets are isolated, its role becomes more ambiguous when the markets are interconnected. However, our numerical simulations suggest that increasing the bias has generally a destabilizing effect